Year 5: Prime factors and factor trees

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. In a factor tree, the two numbers on the branches multiply to make the number above them. Use this to find each missing number: multiply the two numbers below, or divide the number above.

1. Look at what each branch shows. Each number is split into a factor pair.
   Number above = number on the left × number on the right
2. Find the missing numbers. Use multiplying or dividing, whichever you can do.
   The top number 20 is split into ? × 5. So ? = 20 ÷ 5 = 4.
3. Write the missing numbers. List them in the order of the boxes (top to bottom, left to right).
   4

Check. Multiply the circled primes at the bottom: 2 × 2 × 5 = 20. ✓

Watch out. Every number at the end of a branch must be prime.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. In a factor tree, the two numbers on the branches multiply to make the number above them. Use this to find each missing number: multiply the two numbers below, or divide the number above.

1. Look at what each branch shows. Each number is split into a factor pair.
   Number above = number on the left × number on the right
2. Find the missing numbers. Use multiplying or dividing, whichever you can do.
   The top number 18 is split into ? × 3. So ? = 18 ÷ 3 = 6.
   The top number 6 is split into ? × 2. So ? = 6 ÷ 2 = 3.
3. Write the missing numbers. List them in the order of the boxes (top to bottom, left to right).
   6, 3

Check. Multiply the circled primes at the bottom: 2 × 3 × 3 = 18. ✓

Watch out. Every number at the end of a branch must be prime.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. In a factor tree, the two numbers on the branches multiply to make the number above them. Use this to find each missing number: multiply the two numbers below, or divide the number above.

1. Look at what each branch shows. Each number is split into a factor pair.
   Number above = number on the left × number on the right
2. Find the missing numbers. Use multiplying or dividing, whichever you can do.
   The top number 45 is split into ? × 5. So ? = 45 ÷ 5 = 9.
   The top number 9 is split into ? × 3. So ? = 9 ÷ 3 = 3.
3. Write the missing numbers. List them in the order of the boxes (top to bottom, left to right).
   9, 3

Check. Multiply the circled primes at the bottom: 3 × 3 × 5 = 45. ✓

Watch out. Every number at the end of a branch must be prime.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   14 = 2 × 7
2. Circle the primes at the ends of the branches. These are the prime factors.
   2, 7
3. Write them in order, joined with ×. The smallest prime goes first.
   14 = 2 × 7

Check. Multiply the primes back together: 2 × 7 = 14. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   21 = 3 × 7
2. Circle the primes at the ends of the branches. These are the prime factors.
   3, 7
3. Write them in order, joined with ×. The smallest prime goes first.
   21 = 3 × 7

Check. Multiply the primes back together: 3 × 7 = 21. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   35 = 5 × 7
2. Circle the primes at the ends of the branches. These are the prime factors.
   5, 7
3. Write them in order, joined with ×. The smallest prime goes first.
   35 = 5 × 7

Check. Multiply the primes back together: 5 × 7 = 35. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   15 = 3 × 5
2. Circle the primes at the ends of the branches. These are the prime factors.
   3, 5
3. Write them in order, joined with ×. The smallest prime goes first.
   15 = 3 × 5

Check. Multiply the primes back together: 3 × 5 = 15. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   24 = 2 × 12
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   12 = 2 × 6
   6 = 2 × 3
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 2, 3
4. Write them in order, joined with ×. The smallest prime goes first.
   24 = 2 × 2 × 2 × 3

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 3 = 24. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   40 = 2 × 20
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   20 = 2 × 10
   10 = 2 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 2, 5
4. Write them in order, joined with ×. The smallest prime goes first.
   40 = 2 × 2 × 2 × 5

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 5 = 40. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   45 = 3 × 15
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   15 = 3 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   3, 3, 5
4. Write them in order, joined with ×. The smallest prime goes first.
   45 = 3 × 3 × 5

Check. Multiply the primes back together: 3 × 3 = 9, 9 × 5 = 45. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   50 = 2 × 25
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   25 = 5 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 5, 5
4. Write them in order, joined with ×. The smallest prime goes first.
   50 = 2 × 5 × 5

Check. Multiply the primes back together: 2 × 5 = 10, 10 × 5 = 50. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   60 = 2 × 30
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   30 = 2 × 15
   15 = 3 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 3, 5
4. Write them in order, joined with ×. The smallest prime goes first.
   60 = 2 × 2 × 3 × 5

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 3 = 12, 12 × 5 = 60. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   63 = 3 × 21
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   21 = 3 × 7
3. Circle the primes at the ends of the branches. These are the prime factors.
   3, 3, 7
4. Write them in order, joined with ×. The smallest prime goes first.
   63 = 3 × 3 × 7

Check. Multiply the primes back together: 3 × 3 = 9, 9 × 7 = 63. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   72 = 2 × 36
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   36 = 2 × 18
   18 = 2 × 9
   9 = 3 × 3
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 2, 3, 3
4. Write them in order, joined with ×. The smallest prime goes first.
   72 = 2 × 2 × 2 × 3 × 3

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 3 = 24, 24 × 3 = 72. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   80 = 2 × 40
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   40 = 2 × 20
   20 = 2 × 10
   10 = 2 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 2, 2, 5
4. Write them in order, joined with ×. The smallest prime goes first.
   80 = 2 × 2 × 2 × 2 × 5

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, 16 × 5 = 80. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   90 = 2 × 45
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   45 = 3 × 15
   15 = 3 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 3, 3, 5
4. Write them in order, joined with ×. The smallest prime goes first.
   90 = 2 × 3 × 3 × 5

Check. Multiply the primes back together: 2 × 3 = 6, 6 × 3 = 18, 18 × 5 = 90. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   96 = 2 × 48
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   48 = 2 × 24
   24 = 2 × 12
   12 = 2 × 6
   6 = 2 × 3
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 2, 2, 2, 3
4. Write them in order, joined with ×. The smallest prime goes first.
   96 = 2 × 2 × 2 × 2 × 2 × 3

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, 16 × 2 = 32, 32 × 3 = 96. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   98 = 2 × 49
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   49 = 7 × 7
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 7, 7
4. Write them in order, joined with ×. The smallest prime goes first.
   98 = 2 × 7 × 7

Check. Multiply the primes back together: 2 × 7 = 14, 14 × 7 = 98. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Multiply the prime factors together, two at a time, from left to right.

1. Write the product. These are the prime factors of the number.
   2 × 2 × 3
2. Multiply two at a time. Use the answer to each step in the next step.
   2 × 2 = 4
   4 × 3 = 12
3. Write the number.
   2 × 2 × 3 = 12

Check. Go backwards and divide 12 by each prime in turn: 12 ÷ 2 = 6, 6 ÷ 2 = 3, 3 ÷ 3 = 1. We reach 1. ✓

Watch out. Multiply the numbers. Do not add them.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Multiply the prime factors together, two at a time, from left to right.

1. Write the product. These are the prime factors of the number.
   2 × 3 × 5
2. Multiply two at a time. Use the answer to each step in the next step.
   2 × 3 = 6
   6 × 5 = 30
3. Write the number.
   2 × 3 × 5 = 30

Check. Go backwards and divide 30 by each prime in turn: 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1. We reach 1. ✓

Watch out. Multiply the numbers. Do not add them.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Multiply the prime factors together, two at a time, from left to right.

1. Write the product. These are the prime factors of the number.
   3 × 3 × 5
2. Multiply two at a time. Use the answer to each step in the next step.
   3 × 3 = 9
   9 × 5 = 45
3. Write the number.
   3 × 3 × 5 = 45

Check. Go backwards and divide 45 by each prime in turn: 45 ÷ 3 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1. We reach 1. ✓

Watch out. Multiply the numbers. Do not add them.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Multiply the prime factors together, two at a time, from left to right.

1. Write the product. These are the prime factors of the number.
   2 × 2 × 2 × 7
2. Multiply two at a time. Use the answer to each step in the next step.
   2 × 2 = 4
   4 × 2 = 8
   8 × 7 = 56
3. Write the number.
   2 × 2 × 2 × 7 = 56

Check. Go backwards and divide 56 by each prime in turn: 56 ÷ 2 = 28, 28 ÷ 2 = 14, 14 ÷ 2 = 7, 7 ÷ 7 = 1. We reach 1. ✓

Watch out. Multiply the numbers. Do not add them.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   36 = 2 × 18
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   18 = 2 × 9
   9 = 3 × 3
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 3, 3
4. List each different prime once. The question asks for the prime factors, not the whole product.
   36 = 2 × 2 × 3 × 3, so the prime factors are 2 and 3

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 3 = 12, 12 × 3 = 36. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   100 = 2 × 50
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   50 = 2 × 25
   25 = 5 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 5, 5
4. List each different prime once. The question asks for the prime factors, not the whole product.
   100 = 2 × 2 × 5 × 5, so the prime factors are 2 and 5

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 5 = 20, 20 × 5 = 100. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   75 = 3 × 25
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   25 = 5 × 5
3. Circle the primes at the ends of the branches. These are the prime factors.
   3, 5, 5
4. List each different prime once. The question asks for the prime factors, not the whole product.
   75 = 3 × 5 × 5, so the prime factors are 3 and 5

Check. Multiply the primes back together: 3 × 5 = 15, 15 × 5 = 75. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   84 = 2 × 42
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   42 = 2 × 21
   21 = 3 × 7
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 3, 7
4. List each different prime once. The question asks for the prime factors, not the whole product.
   84 = 2 × 2 × 3 × 7, so the prime factors are 2, 3 and 7

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 3 = 12, 12 × 7 = 84. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   48 = 6 × 8
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   6 = 2 × 3
   8 = 2 × 4
   4 = 2 × 2
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 3, 2, 2, 2
4. Write them in order, joined with ×. The smallest prime goes first.
   48 = 2 × 2 × 2 × 2 × 3

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, 16 × 3 = 48. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Split the number into factors with a factor tree. Keep going until every branch ends in a prime number. The primes at the ends are the prime factors.

1. Split the number into a factor pair. Pick any factor pair you know from the times tables.
   48 = 4 × 12
2. Keep splitting every number that is not prime. A number that is not prime can be split again. Stop on a prime: it cannot be split.
   4 = 2 × 2
   12 = 2 × 6
   6 = 2 × 3
3. Circle the primes at the ends of the branches. These are the prime factors.
   2, 2, 2, 2, 3
4. Write them in order, joined with ×. The smallest prime goes first.
   48 = 2 × 2 × 2 × 2 × 3

Check. Multiply the primes back together: 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, 16 × 3 = 48. ✓

Watch out. Every branch must end in a prime. 9 is not prime (3 × 3), and 1 is never used. You can start with any factor pair: the primes at the end are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. Look at the primes at the bottom of both trees.

1. Compare the two lists. Write the primes in order.
   Sam: 2 × 2 × 2 × 2 × 3
   Mia: 2 × 2 × 2 × 2 × 3
2. Say what you notice.
   The two lists are exactly the same.

Check. 2 × 2 × 2 × 2 × 3 = 48. ✓

Watch out. The starting pair does not matter. The prime factors are always the same.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. 2 × 2 × 3 × 3 is the prime factorisation of 36. A number is a factor of 36 if you can build it from some of these primes.

1. Write 12 as a product of primes. Use a factor tree.
   12 = 2 × 2 × 3
2. Check that 36 has all the primes you need. You need the same number of each prime, or more.

   Prime	Needed for 12	Available in 36	Enough?
   2	2	2	yes
   3	1	2	yes

3. Answer the question.
   12 is a factor of 36: Yes

Check. 36 ÷ 12 = 3. ✓

Watch out. You can only use each prime as many times as it appears.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. 2 × 2 × 3 × 3 is the prime factorisation of 36. A number is a factor of 36 if you can build it from some of these primes.

1. Write 8 as a product of primes. Use a factor tree.
   8 = 2 × 2 × 2
2. Check that 36 has all the primes you need. You need the same number of each prime, or more.

   Prime	Needed for 8	Available in 36	Enough?
   2	3	2	no

3. Answer the question.
   8 is not a factor of 36: No

Check. 36 ÷ 8 = 4 remainder 4. ✓

Watch out. You can only use each prime as many times as it appears.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. 2 × 2 × 3 × 3 is the prime factorisation of 36. A number is a factor of 36 if you can build it from some of these primes.

1. Write 18 as a product of primes. Use a factor tree.
   18 = 2 × 3 × 3
2. Check that 36 has all the primes you need. You need the same number of each prime, or more.

   Prime	Needed for 18	Available in 36	Enough?
   2	1	2	yes
   3	2	2	yes

3. Answer the question.
   18 is a factor of 36: Yes

Check. 36 ÷ 18 = 2. ✓

Watch out. You can only use each prime as many times as it appears.

Key words. A prime factor is a factor that is a prime number. A factor tree splits a number into smaller and smaller factors until every branch ends in a prime. Writing a number as a product of its prime factors is called prime factorisation.

Method. 2 × 2 × 3 × 3 is the prime factorisation of 36. A number is a factor of 36 if you can build it from some of these primes.

1. Write 10 as a product of primes. Use a factor tree.
   10 = 2 × 5
2. Check that 36 has all the primes you need. You need the same number of each prime, or more.

   Prime	Needed for 10	Available in 36	Enough?
   2	1	2	yes
   5	1	0	no

3. Answer the question.
   10 is not a factor of 36: No

Check. 36 ÷ 10 = 3 remainder 6. ✓

Watch out. You can only use each prime as many times as it appears.

Key words. A counter-example is one example that shows a statement is false.

Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.

1. Try some numbers. Test the statement with some examples.
   Even numbers: 6 = 2 × 3, 10 = 2 × 5, 18 = 2 × 3 × 3, 40 = 2 × 2 × 2 × 5
2. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   An even number divides exactly by 2, so 2 is one of its factors. 2 is prime. So 2 is always a prime factor.
3. Decide.
   Always

Check. Try 100: 100 = 2 × 2 × 5 × 5. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.

Key words. A counter-example is one example that shows a statement is false.

Method. Try some examples. If the statement is true for every example you can find, ask why. If you find one that is false, it cannot be “always”.

1. Try some numbers. Test the statement with some examples.
   15 = 3 × 5: 3 is a prime factor and 15 is odd.
2. Look for one that does not work. One example that breaks the rule is called a counter-example.
   6 = 2 × 3: 3 is a prime factor but 6 is even.
3. Explain why. A reason shows what is happening for every number, not just the ones we tried.
   Whether a number is odd or even depends on whether 2 is one of its prime factors, not on whether 3 is.
4. Decide.
   Sometimes

Check. 15 is odd and 6 is even, so we have one of each. ✓

Watch out. “Always” means every time. “Sometimes” needs one example that works and one that does not. “Never” means no example works.