The idea, step by step
Factors fit exactly
Factors name whole-number group sizes that fit a number with no remainder. For 24 counters, groups of 3 work because 3×8=24; groups of 5 leave some over.
To find common factors, list the factors of both numbers and identify shared values. The greatest common factor is useful when the largest equal group, or greatest number of identical bags, must fit two collections.
Multiples form repeating patterns
Multiples are the results of multiplying a number by whole numbers. The positive multiples of 6 begin 6, 12, 18, 24, 30. There is no last multiple.
For repeating events, list the intervals for each event and find the first positive interval they share. If two bells ring together now, zero is the starting time, not the answer to when they next meet.
A common trap
A multiple of 8 must be smaller than 8.
Instead: That confuses multiples with factors. Multiples include 8, 16, 24 and larger values.
See the thinking
Worked example 1
Find the greatest common factor of 18 and 24.
- Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
- The shared factors are 1, 2, 3 and 6; the greatest is 6.
Worked example 2
Two lights flash together now, then every 4 seconds and every 6 seconds. When do they next flash together?
- Multiples of 4 begin 4, 8, 12; multiples of 6 begin 6, 12.
- The first shared positive interval is 12.
Check your understanding
Is 7 a factor of 42 or a multiple of 42?
Show answer
A factor of 42.
7×6=42, so 7 divides 42 exactly.
Your turn
6 questions · 12 marks · Work at your own pace.
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 6×4=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÷6=5 and 42÷6=7.
6 bags, each with 5 red and 7 blue beads. - Correct this sentence: 4 is a multiple of 20.2 marks
4×5=20.
4 is a factor of 20, or 20 is a multiple of 4.
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 ↗