Factors, Hcf And Lcm

FACTORS

The factors of a number are all the numbers that divide into the number.

Example

Find the factors of 64.

Start with 1, then 2, then 3 etc to see if it goes into 64. If it does, write down the number that you need to multiply by. If it doesn`t, leave a blank in the right hand column. Continue until we get a repeat.

1 x 64

2 x 32

3 x

4 x 16

5 x

6 x

7 x

8 x 8

So the factors of 64 are 1, 2, 4, 8, 16, 32 and 64.

The Highest Common Factor (HCF) of two numbers is the highest number that will divide exactly into the two numbers in question.

Example

Find the highest common factor of 64 and 24.

We know that the factors of 64 are 1, 2, 4, 8, 16, 32 and 64. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The highest number common to both lists is 8 so 8 is the HCF.

Don`t confuse the HCF with the LCM, the Lowest Common Multiple, which is the smallest number that the two numbers in question will divide into.

Example

What is the lowest common multiple of 64 and 24?

We need to start going through multiples of each number, starting with 24. We get 24, 48, 72, 96, 120, 144, 168, 192, etc etc. For 64 we get 64, 128, 192, etc etc. The lowest number common to both lists is 192 so the LCM is 192.