 # Find factor pairs (below 100)

Lesson

In the statement $3\times5=15$3×5=15 we have a product (which is the answer of $15$15), and a factor pair of $3$3 and $5$5. The numbers that multiply together to give us the product are factors, when we have 2 of them that multiply to give us a product they are a factor pair.  There is another factor pair for 15.  Can you find it?

Sometimes there is more than one factor pair.  For example, the number 12. Could be written as

$2\times6=12$2×6=12

$3\times4=12$3×4=12

$1\times12=12$1×12=12

So $12$12 has $3$3 factor pairs.  2 and 6, 1 and 12, 3 and 4.

Every number will have at least one factor pair.  Prime numbers have only one factor pair, of $1$1 and itself. For example $7$7.  It's only factor pair is $1$1 and $7$7.

##### Example 1 - Using a multiplication table

Let's find the factor pairs for the number $6$6.

$\times$× $1$1 $2$2 $3$3 $4$4 $5$5 $6$6
$1$1 $1$1 $2$2 $3$3 $4$4 $5$5 $6$6
$2$2 $2$2 $4$4 $6$6 $8$8 $10$10 $12$12
$3$3 $3$3 $6$6 $9$9 $12$12 $15$15 $18$18
$4$4 $4$4 $8$8 $12$12 $16$16 $20$20 $24$24
$5$5 $5$5 $10$10 $15$15 $20$20 $25$25 $30$30
$6$6 $6$6 $12$12 $18$18 $24$24 $30$30 $36$36

Using the table we can find all the numbers that multiply to give $6$6. We will only count factor pairs once, so, $1\times6$1×6is the same as $6\times1$6×1. So $1$1 and $6$6 are one set of factors for the number $6$6

Using the table, what are the other factor pairs of $6$6

Using the table we can look for all the numbers that multiply together to give $6$6.

The factor pairs of 6 are:

• 1 and 6, &
• 2 and 3.

#### Examples

##### Question 1

$59$59 is a prime number.

1. Which of the following options is a factor pair of $59$59?

$56$56 and $3$3

A

$1$1 and $59$59

B

##### Question 2

If we multiply $4$4 by $14$14, we get $56$56, so $4$4 and $14$14 make a factor pair of $56$56.

1. Which of the following options is also a factor pair of $56$56?

$14$14 and $2$2

A

$4$4 and $7$7

B

$8$8 and $7$7

C

$2$2 and $2$2

D

##### Question 3

Complete the table below, listing all factor pairs of the number $15$15.

1. Factor pairs of $15$15
$\left(1,\editable{}\right)$(1,)
$\left(\editable{},5\right)$(,5)
2. Is $15$15 prime or composite?

$15$15 is a composite number.

A

$15$15 is a prime number.

B

### Outcomes

#### NA4-1

Use a range of multiplicative strategies when operating on whole numbers