Into it, or out of it? factors and multiples
The Short Answer
A factor divides exactly into a number. A multiple comes out of it, by multiplying. Those two get swapped more often than any other pair of words in maths, so say which direction you are going before answering. Find factors in pairs — one and thirty-six, two and eighteen — and stop when a pair repeats itself, and none will be missed.
The two words that get swapped
More often than any other pair in maths.
Factors divide exactly INTO a number. Multiples come OUT of it, by multiplying.
If a question asks for a factor of six and your child writes twelve, they have given a multiple. They have not made a mistake about numbers — they know six twos are twelve. They have gone the wrong direction.
So the habit is to say the direction before writing anything. Into it, or out of it?
Find factors in pairs
Common factors and common multiples
Same idea, opposite direction.
A common factor is one that two numbers share. 12 and 18 share 1, 2, 3 and 6.
A common multiple is a number that both divide into. 24 is a common multiple of 4, 6 and 8.
Shared factors, shared multiples. Saying it like that makes it one idea rather than two rules to remember.
One useful asymmetry
Every number has a limited list of factors and an endless list of multiples.
Nothing bigger than 36 can divide into 36, so the factor list has to stop. But 36, 72, 108, 144 — the multiples never run out.
That gives your child an instant check: an answer for factors that looks like it could keep going is wrong.
Where do pupils lose marks?
Swapping the two words, which is the whole difficulty of the topic.
Missing a factor in the middle, by hunting rather than pairing.
Listing the pair 6 × 6 twice.
Giving a common multiple when common factors were asked for.
Try it yourself
Say which direction you are going — into it, or out of it — before you write anything.
- List all the factors of 36.
- How many factors does 36 have?
- What are the common factors of 12 and 18?
- Is 24 a common multiple of 4, 6 and 8?
- A question asks for a factor of 6 and a child writes 12. What have they given?
- 1, 2, 3, 4, 6, 9, 12, 18, 36. Found in pairs: 1×36, 2×18, 3×12, 4×9, 6×6 — and once the pair repeats itself you stop, because everything after it is a repeat.
- Nine. Note that 6 appears only once even though it comes from the pair 6×6.
- 1, 2, 3 and 6. List the factors of each and see which appear in both. These are the numbers that divide into both.
- Yes. 24 ÷ 4 = 6, 24 ÷ 6 = 4 and 24 ÷ 8 = 3, all exact. A common multiple is a number all of them divide into.
- A multiple. Twelve comes out of six by multiplying; it does not go into it. This is the single commonest error on the topic and it is a vocabulary error rather than a maths one.
How much practice does this type need at home?
Times tables, mostly. A child with instant recall finds factors quickly because they recognise 36 as 4 × 9 without calculating; a child who has to work it out is slow at every question in this family.
Beyond that, one drill: say a number and ask for all its factors, in pairs, out loud. Twenty-four. One and twenty-four, two and twelve, three and eight, four and six — stop. Fifteen seconds, and it builds the pairing habit that makes the rest automatic.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
How do I stop my child swapping the two words?
Give them a direction rather than a definition. Factors go INTO a number. Multiples come OUT of it. Saying which direction they are travelling before they write anything catches it, and the mistake is nearly always a vocabulary slip rather than a failure of arithmetic — a child who writes 12 as a factor of 6 knows perfectly well that 6 × 2 = 12.
Why find factors in pairs?
Because it guarantees none are missed and it tells you when to stop. Work upwards — 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 — and as soon as a pair repeats itself, every remaining possibility has already been listed. Children who hunt for factors one at a time reliably miss one in the middle, and have no way of knowing they have finished.
What is the difference between a common factor and a common multiple?
Same idea, opposite direction. A common factor is a number that divides into both — 12 and 18 share 1, 2, 3 and 6. A common multiple is a number that both divide into — 24 is a common multiple of 4, 6 and 8. Shared factors, shared multiples. Saying it that way makes them one idea rather than two rules.
Does a number have more factors or more multiples?
More multiples, always — the list of multiples never ends, since you can keep multiplying. The list of factors always stops, because nothing bigger than the number can divide into it. That is worth saying, because it gives a child an instant check: if they have written an endless-looking answer for factors, something is wrong.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
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