Factor pairs | Year 5 | Ascent Library

01 / LEARN

Understand the idea.

Two factors make one product

A factor pair consists of two positive whole numbers whose product is the target number. Since $3 \times 8 = 24$ , both $3$ and $8$ divide $24$ exactly. A rectangle with $3$ rows of $8$ counters shows that pair.

Turning the rectangle gives $8$ rows of $3$ . The order changes, but the pair uses the same two factors. When listing different factor pairs, record $3 \times 8$ once rather than also counting $8 \times 3$ as a new pair.

Different rectangular arrangements of 24 counters
Rows	Counters in each row	Total
1	24	24
2	12	24
3	8	24
4	6	24

Keep a list so no pair is missed

Search in order so that no pair is missed. Begin with $1$ and the target number, then test $2$ , $3$ , and so on. Record a pair only when the division leaves no remainder; a near fit is not a factor.

Once the smaller and larger partners would cross, later pairs repeat earlier ones. For $24$ , the pairs are $1 \times 24$ , $2 \times 12$ , $3 \times 8$ and $4 \times 6$ . Collect both members to list all factors; zero cannot divide the target.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find the pairs for eighteen

Find all positive factor pairs of 18.

Worked solution

1
Start with one and the whole target.
$1 \times 18 = 18$
1 and 18 are always positive factors of 18.
2
Test the next small whole numbers.
$2 \times 9 = 18, 3 \times 6 = 18$
Both products equal 18 exactly, so both pairs belong in the list.
3
Check the gap before the pairs repeat.
$18 = 4 \times 4 + 2, 18 = 5 \times 3 + 3$
4 and 5 leave remainders; at 6, the partner is the already recorded 3.
4
List each pair once.
$1 \times 18, 2 \times 9, 3 \times 6$
Every smaller candidate up to the repeated pairs has been checked.

Answer

1 × 18, 2 × 9 and 3 × 6.

EXAMPLE 02

Choose a rectangular seating plan

Twenty counters must form a rectangle with at least two rows and at least two counters in each row. Give the possible factor pairs.

Worked solution

1
List the factor pairs of twenty.
$1 \times 20 = 20, 2 \times 10 = 20, 4 \times 5 = 20$
These are the distinct whole-number rectangular arrangements, ignoring turns.
2
Apply the minimum-size condition.
$1 < 2$
The one-row arrangement fails the requirement of at least two rows.
3
Keep the pairs that satisfy both conditions.
$2 \times 10, 4 \times 5$
Both factors in each remaining pair are at least 2.

Answer

2 × 10 and 4 × 5.

03 / YOUR TURN

Try it yourself.

Check your understanding

Is 7 a factor of 28? Give a multiplication fact.

Show answer & reasoning

Yes: 7 × 4 = 28.

Yes: $7 \times 4 = 28$ . This shows $28 \div 7 = 4$ with no remainder, so $7$ is a factor of $28$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

List all positive factor pairs of 12.
2 marks
List the positive factors of 15 in order.
2 marks
Is 6 a factor of 42? Explain.
1 mark
Is 5 a factor of 32? Explain.
1 mark
List each factor pair of 36 once, including the equal-factor pair.
2 marks
A garden has 30 square tiles. It must have at least three rows and at least three tiles per row. Give all possible rectangular factor pairs, ignoring turns.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

List all positive factor pairs of 12.
2 marks
Try one, two and three. Four would repeat three and four.
$1 \times 12$ , $2 \times 6$ and $3 \times 4$ .
List the positive factors of 15 in order.
2 marks
Use $1 \times 15$ and $3 \times 5$ .
1, 3, 5, 15.
Is 6 a factor of 42? Explain.
1 mark
$6 \times 7 = 42$ , so division by six leaves no remainder.
Yes.
Is 5 a factor of 32? Explain.
1 mark
$5 \times 6 = 30$ and $5 \times 7 = 35$ . Neither is thirty-two.
No.
List each factor pair of 36 once, including the equal-factor pair.
2 marks
Five does not divide thirty-six. The pair six and six is included once.
$1 \times 36$ , $2 \times 18$ , $3 \times 12$ , $4 \times 9$ and $6 \times 6$ .
A garden has 30 square tiles. It must have at least three rows and at least three tiles per row. Give all possible rectangular factor pairs, ignoring turns.
3 marks
The pairs are $1 \times 30$ , $2 \times 15$ , $3 \times 10$ and $5 \times 6$ .
Remove pairs with a side shorter than three.
$3 \times 10$ and $5 \times 6$ .

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

Factor pairs; multiples; divisibility; factor/divisibility algorithms.

Official curriculum source ↗

In this lesson

Understand the idea.

Two factors make one product

Keep a list so no pair is missed

See the method in action.

Find the pairs for eighteen

Start with one and the whole target.

Test the next small whole numbers.

Check the gap before the pairs repeat.

List each pair once.

Choose a rectangular seating plan

List the factor pairs of twenty.

Apply the minimum-size condition.

Keep the pairs that satisfy both conditions.

Try it yourself.

Check your understanding

Keep practising