Multiples and Factors: The Difference, How to Find Them

A multiple is the result of multiplying a number by a whole number. A factor is a number that divides another exactly. Both are taught together in Year 4, and precisely because they are taught together they get confused most often.

The Distinction That Never Fails

A hook that sticks: multiples come from multiplying, so they grow. Factors divide, so they shrink.

Finding Multiples

Multiply the number by 1, 2, 3 and so on.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...

The list never ends. If a question asks for "multiples of 4 below 30", the answer is 4, 8, 12, 16, 20, 24, 28.

Finding Factors

Find every number that divides exactly with no remainder. The tidiest method is working in pairs:

Factors of 24:

• 1 × 24
• 2 × 12
• 3 × 8
• 4 × 6
• 5? does not divide, skip
• 6 × 4 — already seen, so stop

So the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 — eight of them.

Stop when the pairs start repeating. This trick halves the work and prevents missing a factor, which is the most common error in the topic.

Divisibility Tests

Knowing these makes factor-hunting much faster:

Example: is 342 divisible by 3? Its digits sum to 3+4+2 = 9, and 9 is divisible by 3 — so yes.

The Link to LCM and HCF

This is where the two ideas meet:

• LCM = Lowest Common Multiple — the smallest multiple two numbers share
• HCF = Highest Common Factor — the largest factor two numbers share

For 12 and 18:

• Multiples of 12: 12, 24, 36, 48 — multiples of 18: 18, 36, 54 → LCM = 36
• Factors of 12: 1, 2, 3, 4, 6, 12 — factors of 18: 1, 2, 3, 6, 9, 18 → HCF = 6

Faster methods are in prime factorisation and how to find the LCM and HCF.

The Mistakes That Actually Cost Marks

1. Confusing multiples with factors. The number one cause, and instantly checkable: if the answers are larger than the original number, the child is finding multiples, not factors.

2. Missing a factor. Usually from searching at random rather than in pairs. The pairing method closes that gap.

3. Forgetting 1 and the number itself. Both are always factors.

4. Thinking there are infinitely many factors. Factors are always finite; multiples are infinite.

5. Confusing LCM with HCF. A hook: LCM uses multiples and gives a large answer; HCF uses factors and gives a small one.