Year 6 · HCF, LCM and Prime Numbers · Summary

Year 6 HCF, LCM and Prime Numbers: summary and key words

Part of the Year 6 hcf, lcm and prime numbers chapter. Chapter overview · whole chapter on one page

Chapter summary

Skill	Method
Factors and factor pairs	Find pairs of numbers that multiply to make the number. Each pair gives two factors.
Common factors and HCF	List the factors of each number and find the ones they share. The HCF is the biggest one. With prime factors, use the shared primes with the smallest powers.
Multiples and LCM	List the multiples of each number until you find the first one in both lists. With prime factors, use every prime with the largest power.
Prime numbers	A prime has exactly two factors, 1 and itself. To test a number, divide by the primes up to its square root.
Factor trees and index form	Split the number into factors until every branch is prime. Write repeated primes with a power.
Choosing HCF or LCM	Use the HCF for the largest equal groups, pieces or tiles. Use the LCM for the smallest number that fits, or when things happen together again.

I can list all the factors of a number, using factor pairs.
I can find the common factors of two numbers and the highest common factor (HCF).
I can list common multiples and find the lowest common multiple (LCM).
I can say whether a number up to 100 is prime, and I know the primes up to 20.
I can write a number as a product of prime factors, using a factor tree and index form.
I can use prime factors to find the HCF and the LCM.
I can solve problems by choosing the HCF or the LCM, and explain my choice.
I can say whether a statement is always, sometimes or never true, and give an example.

Factor: A number that divides into another number exactly, with no remainder.
Common factor: A factor of two or more numbers.
Highest common factor (HCF): The biggest common factor of two or more numbers.
Multiple: An answer in a times table, such as 6, 12, 18 for the multiples of 6.
Common multiple: A number that is a multiple of two or more numbers.
Lowest common multiple (LCM): The smallest common multiple of two or more numbers.
Prime number: A number with exactly two factors: 1 and itself. 1 is not prime.
Composite number: A whole number greater than 1 that is not prime.
Prime factor: A factor of a number that is also a prime number.
Factor tree: A diagram that splits a number into factors until every branch is prime.
Index form: A way of writing repeated multiplication with a power, such as 2³ = 2 × 2 × 2.
Counter-example: One example that shows a statement is not always true.