A multiple of 6 is in the 6 times table: 6, 12, 18 and so on. A factor of 36 divides 36 exactly. To find all the factors, list factor pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6. Every number has 1 and itself as factors. In a square number the middle pair repeats a factor, so count it once.
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Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- factor
- a whole number that divides another exactly
- multiple
- the result of multiplying a number by a whole number
- factor pair
- two factors that multiply to make the number
Worked examples
Which of these numbers is a multiple of 6? 3, 16, 36, 15
- 1.Divide each by 6: only 36 divides exactly.
- 2.6 × 6 = 36.
= 36
How many factors does 36 have?
- 1.Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
- 2.Count 6 once: 1, 2, 3, 4, 6, 9, 12, 18, 36.
= 9
I am a multiple of 6. I am a factor of 72. I am between 20 and 30. What number am I?
- 1.Multiples of 6 between 20 and 30: 24.
- 2.24 is a factor of 72, since 72 = 3 × 24.
= 24
For parents
Method: Factor pairs
What to say: Does it divide exactly? Have you found every pair?
Common mistakes:
- Mixes up factors and multiples: picks a number that goes into n instead of one n goes into.
- Thinks a number ending in the same digit is a multiple (16 for 6), overusing the 5s and 10s rule.
- Picks a multiple of one of n's factors (15 for 6, because it is in the 3 times table).
- Counts the repeated factor of a square number twice (6 × 6 gives 6 and 6).
- Forgets that 1 and the number itself are factors.
- Counts the factor pairs instead of the factors.
- Uses only the multiple and range clues, ignoring 'I am a factor of …'.
- Uses only the factor and range clues, ignoring 'I am a multiple of …'.
- Gives a number that fits the factor and multiple clues but is outside the given range.