Year 5 · Prime Numbers, Factors, Squares and Cubes · Summary

Year 5 Prime Numbers, Factors, Squares and Cubes: summary and key words

Part of the Year 5 prime numbers, factors, squares and cubes chapter. Chapter overview · whole chapter on one page

Chapter summary

Skill	Method
Multiples	Multiply the number by 1, 2, 3, 4… (count on in its steps). To test a number, look at the multiples just below and just above it, or divide: no remainder means it is a multiple.
Common multiples and LCM	List the multiples of both numbers. The numbers in both lists are common multiples. The smallest is the lowest common multiple (LCM). Use it for buses, lights and bells that repeat.
Tests of divisibility	2: last digit even. 3: digits add to a multiple of 3. 4: last two digits in the 4s (or halve twice). 5: ends in 0 or 5. 6: passes 2 and 3. 8: halve three times. 9: digits add to a multiple of 9. 10: ends in 0. 25: ends in 00, 25, 50, 75. 100: ends in 00.
Factors and factor pairs	Start with 1 × the number. Try 2, 3, 4… in order and write each pair that divides exactly. Stop when the pairs meet. Write the factors in order. Square numbers have an odd number of factors.
Common factors and HCF	List the factors of both numbers. The numbers in both lists are the common factors. The biggest is the highest common factor (HCF). Use it for sharing into equal groups with none left over.
Prime and composite numbers	Prime: exactly two factors (1 and itself). Composite: more than two factors. 1 is neither. 2 is the only even prime. Primes to 19: 2, 3, 5, 7, 11, 13, 17, 19.
Is a number up to 100 prime?	Test with 2, 3, 5 and 7. If one divides it (and the number is not that prime itself), it is composite. If none does, it is prime. The sieve crosses out the multiples of 2, 3, 5 and 7.
Prime factors and factor trees	Split the number into a factor pair, split again, and stop on primes. Write the primes in order with × between them: 60 = 2 × 2 × 3 × 5. Check by multiplying.
Square numbers	n² = n × n. Know 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and 15² = 225, 20² = 400, 25² = 625, 30² = 900. The little 2 does not mean “times 2”.
Cube numbers	n³ = n × n × n. Know 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000. The little 3 does not mean “times 3”.
Clues and reasoning	For a clue puzzle, start with the clue that gives the shortest list, cross out, then check every clue. “Always” needs a reason; “sometimes” needs two examples; one counter-example breaks “always”.

Can you…?

I can list multiples of a number and decide whether a number is a multiple of another.
I can find common multiples and the lowest common multiple, and use them to solve problems about things that repeat.
I can use the tests of divisibility for 2, 3, 4, 5, 6, 8, 9, 10, 25 and 100.
I can find all the factor pairs of a number in order, and list its factors.
I can find common factors and the highest common factor of two numbers.
I know what prime and composite numbers are, and I know the primes up to 19.
I can decide whether a number up to 100 is prime.
I can write a number up to 100 as a product of prime factors using a factor tree.
I can work out squares (up to 12 × 12 and beyond) and cubes, and use the ² and ³ notation.
I can solve clue puzzles and explain my reasoning: always, sometimes, never; prove it; spot the mistake.

Key terms

Multiple: A number in the times table of another number. The multiples of 5 are 5, 10, 15, 20…
Common multiple: A number that is a multiple of two (or more) numbers.
Lowest common multiple (LCM): The smallest common multiple. The LCM of 4 and 6 is 12.
Divisible: A number is divisible by another if it divides exactly, with no remainder.
Test of divisibility: A quick rule, using the digits, to find out whether a number is divisible by another.
Factor: A whole number that divides exactly into another number. The factors of 6 are 1, 2, 3 and 6.
Factor pair: Two factors that multiply to make a number: 2 and 3 are a factor pair of 6.
Common factor: A number that is a factor of two (or more) numbers.
Highest common factor (HCF): The biggest common factor. The HCF of 12 and 18 is 6.
Prime number: A number with exactly two factors: 1 and itself. 2, 3, 5, 7, 11…
Composite number: A number with more than two factors, such as 12. (1 is neither prime nor composite.)
Prime factor: A factor that is a prime number. The prime factors of 12 are 2 and 3.
Factor tree: A diagram that splits a number into factors until every branch ends in a prime number.
Product: The answer to a multiplication. 2 × 2 × 3 is a product of primes.
Square number: A number multiplied by itself, such as 25 = 5 × 5. Written 5².
Cube number: A number multiplied by itself twice, such as 125 = 5 × 5 × 5. Written 5³.
Sieve of Eratosthenes: A way of finding primes on a hundred square by crossing out the multiples of 2, 3, 5 and 7.
Counter-example: One example that shows a statement is false.
Array: Objects arranged in equal rows and columns. It shows a multiplication and a factor pair.