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# Factors

### Factors

Factors are each of the numbers which we can divide another number by, and get a whole number.

A **factor** perfectly divides a number, leaving a whole number with no remainder.

When you divide $16$ by any of these numbers, the answer is whole.

$1,2,4,8,16$

What is $16\div1$?

What is $16\div2$?

What is $16\div4$?

These are all factors of $16$

Similarly, we can **multiply** pairs of these together to regenerate $16$. For example, $2 \times 8 = 16$ and $1 \times 16 = 16$.

Which of the following is NOT a factor of $15$?

It's useful to identify factors of a number and list them in order without skipping any.

Let's find the factors of $80$

We could try out random numbers

But this could take a while, and we could miss a factor out by accident.

We need a more systematic method

Let's find factor pairs of $80$, using multiplication facts, starting with $1$.

What, multiplied by $1$, gives the answer $80$?

The first multiplication is $1 \times 80$

Since both numbers multiply together to make $80$ (and as a result, they both also divide $80$ to give a whole number), they are both **FACTORS**.

What, multiplied by $2$, gives $80$?

We have $1, 2, 40, 80$ as factors

Let's keep going systematically to find all the factors.

Does $80$ divide by $3$ to give a whole number?

$3$ is not a factor

It can't divide $80$ to leave a whole number.

$4,5,8$ are also factors

Each of these numbers divide $80$ to leave a whole number.

Is $9$ a factor of $80$?

$9$ isn't a factor

We have all the factors!

$1, 2, 4, 5, 8, 10, 16, 20, 40, 80$

Let's try listing all the factors of $24$.

Start by dividing by $1$

We know a multiplication fact is $1 \times 24$

Next, try dividing $24 \div 2$.

Divide $24 \div 3$

Divide $24 \div 4$

Is $5$ a factor? (Yes/No)

We have them all!

6 is the next number we'd try, and it's already in the list. The factors of$24$ are:

$1, 2, 3, 4, 6, 8, 12, 24$.

What are ALL the factors of 10?

If two numbers share a factor, this is known as a **common factor**.

For example, let's look at the factors of $12$ and $15$

List all the factors of $12$

$1, 2, 3, 4, 6, 12$

List all the factors of $15$

$1, 3, 5, 15$

You will notice that both numbers share the factor of $1$

But this is not the only common factor.

Other than $1$, what other factor is shared by the two numbers?

$12$ and $15$ have two common factors

Since $1$ and $3$ are factors of both numbers, they are **common factors**.

Find a common factor of $32$ and $40$.