# Factors

Lesson

A number may be made by multiplying two other numbers together. The numbers that are multiplied together are called factors of the final number. All numbers have factors of one and themselves

$1\times7=7$1×7=7

$1\times14=14$1×14=14 and so on.

## How do we test if a number is a factor of another number?

If you can divide a whole number by another whole number and the answer is a whole number, then it is a factor. Let's look at an example to explain what I mean.

#### Examples

##### Question 1

Evaluate: Is $15$15 a factor of $45$45?

Think: $45\div15=3$45÷​15=3 (this answer is a whole number).

DoYes, $15$15 is a factor of $45$45 (and so is $3$3)

However, some numbers have more factors than others.

$5$5 only has factors of $1$1 and $5$5 but

$12$12 can be made up as $1\times12$1×12, $2\times6$2×6 and $3\times4$3×4. So the factors of $12$12 are $1,2,3,4,6$1,2,3,4,6 and $12$12.

##### Question 2

Write down all the factors of $144$144

Think: $1\times144$1×144, $2\times72$2×72, $3\times48$3×48, $4\times36$4×36, $6\times24$6×24, $8\times18$8×18, $9\times16$9×16 and $12\times12$12×12 all give an answer of $144$144.

So, the factors of $144$144 are $1,2,3,4,6,8,9,12,16,18,24,36,48,72$1,2,3,4,6,8,9,12,16,18,24,36,48,72 and $144$144.

That was a lot!

##### Question 3

Which of these numbers is $6$6 a factor of?

1. $30$30

A

$32$32

B

$17$17

C

$39$39

D

$30$30

A

$32$32

B

$17$17

C

$39$39

D

##### Question 4

Write down all factors of $12$12.

Separate numbers with a comma.

##### Question 5

What is the highest common factor of $24$24 and $36$36?