Factors/multiples revision | Year 6

01 / LEARN

Understand the idea.

Factors fit exactly

A factor is a whole-number group size that fits exactly. For example, $3$ is a factor of $24$ because $3 \times 8 = 24$ . Listing factor pairs is a reliable way to collect all possible group sizes.

A common factor fits both numbers. The greatest common factor is the largest shared value. For identical bags using two collections, the number of bags must divide both totals, so a common factor tells you which bag counts are possible.

Multiples form repeating patterns

A multiple is a result in a times table. The positive multiples of $6$ begin $6, 12, 18, 24$ . Unlike a factor list for a positive number, a list of multiples keeps going without a last value.

When events repeat, list their future times from the same starting point. The first positive common multiple tells you when they next happen together. Zero records the shared start, rather than the next meeting.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Find the greatest common factor of 18 and 24.

Worked solution

1
List the factors of 18.
$18 = 1 \times 18 = 2 \times 9 = 3 \times 6$
The complete list is 1, 2, 3, 6, 9 and 18.
2
List the factors of 24.
$24 = 1 \times 24 = 2 \times 12 = 3 \times 8 = 4 \times 6$
The complete list is 1, 2, 3, 4, 6, 8, 12 and 24.
3
Select the greatest shared factor.
$Common factors: 1, 2, 3, 6$
Both lists contain these values, and 6 is the greatest.

Answer

EXAMPLE 02

Worked example 2

Two lights flash together now, then every 4 seconds and every 6 seconds. When do they next flash together?

Worked solution

1
List the first light’s future flash times.
$4, 8, 12 seconds$
Each flash occurs another 4 seconds after the starting time.
2
List the second light’s future flash times.
$6, 12 seconds$
Each flash occurs another 6 seconds after the starting time.
3
Find the first shared positive time.
$12 = 3 \times 4 = 2 \times 6$
Twelve is the first time in both lists, so the lights next flash together after 12 seconds.

Answer

After 12 seconds.

03 / YOUR TURN

Try it yourself.

Check your understanding

Is 7 a factor of 42 or a multiple of 42?

Show answer & reasoning

A factor of 42.

$7 \times 6 = 42$ , so dividing $42$ by $7$ leaves no remainder. That makes $7$ a factor of $42$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Write the first five positive multiples of 9.
2 marks
Find every common factor of 12 and 20.
2 marks
Is 24 a multiple of 6? Explain.
1 mark
Find the smallest positive common multiple of 5 and 8.
2 marks
There are 30 red beads and 42 blue beads. Make the greatest number of identical bags, using all beads. How many bags and what is in each?
3 marks
Correct this sentence: 4 is a multiple of 20.
2 marks

Read the worked solutions

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

Write the first five positive multiples of 9.
2 marks
Multiply 9 by 1 through 5.
9, 18, 27, 36, 45.
Find every common factor of 12 and 20.
2 marks
Compare their factor lists.
1, 2 and 4.
Is 24 a multiple of 6? Explain.
1 mark
24 appears in the six-times table.
Yes, because $6 \times 4 = 24$ .
Find the smallest positive common multiple of 5 and 8.
2 marks
List multiples until both lists contain 40.
40.
There are 30 red beads and 42 blue beads. Make the greatest number of identical bags, using all beads. How many bags and what is in each?
3 marks
The greatest common factor is 6; $30 \div 6 = 5$ and $42 \div 6 = 7$ .
6 bags, each with 5 red and 7 blue beads.
Correct this sentence: 4 is a multiple of 20.
2 marks
$4 \times 5 = 20$ .
4 is a factor of 20, or 20 is a multiple of 4.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Prime/composite/square numbers; factors/multiples revision; efficient calculation and estimation.

Official curriculum source ↗

In this lesson

Understand the idea.

Factors fit exactly

Multiples form repeating patterns

See the method in action.

Worked example 1

List the factors of 18.

List the factors of 24.

Select the greatest shared factor.

Worked example 2

List the first light’s future flash times.

List the second light’s future flash times.

Find the first shared positive time.

Try it yourself.

Check your understanding

Keep practising