Factors and Multiples
Year 5 · Maths · Free — no account needed
Factors and Multiples
Factors
A factor of a number divides into it evenly, with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12 — each of these divides evenly into 12.
To find all the factors of a number, check every whole number up to it: does it divide in evenly? 1 and the number itself are always factors.
Multiples
A multiple of a number is what you get when you multiply it by a whole number. The multiples of 4 are 4, 8, 12, 16, 20... (4×1, 4×2, 4×3, 4×4, 4×5...). Multiples go on forever.
Products of factors
Every whole number can be written as a product of its factors. 12 = 2 × 6, or 12 = 3 × 4, or 12 = 2 × 2 × 3.
Divisibility
One number is divisible by another if it divides evenly with no remainder. 15 is divisible by 3 (15 ÷ 3 = 5 exactly) but 15 is not divisible by 4 (15 ÷ 4 = 3 remainder 3).
Quick divisibility checks:
- Divisible by 2: the number is even (ends in 0, 2, 4, 6, 8)
- Divisible by 5: ends in 0 or 5
- Divisible by 10: ends in 0
Worked Example
Is 18 a factor or a multiple of 6? Is it both, or neither? 18 ÷ 6 = 3 exactly, so 6 divides evenly into 18 — that makes 6 a factor of 18, and 18 a multiple of 6. Now check: is 18 a factor of 6? 6 ÷ 18 is less than 1, so no — 18 is too big to be a factor of 6. So: 18 is a MULTIPLE of 6 (not a factor of 6).
Practice
What are the factors of 10?
Flashcards
What is a factor?
A number that divides evenly into another number, with nothing left over.
What is a multiple?
The result of multiplying a number by a whole number — multiples go on forever.
Are 1 and the number itself always factors of that number?
Yes — every whole number is divisible by 1 and by itself.
How can you tell if a number is divisible by 2?
It's even — it ends in 0, 2, 4, 6, or 8.
How can you tell if a number is divisible by 5?
It ends in 0 or 5.
If 8 is a factor of 24, what does that make 24?
A multiple of 8 (24 = 8 × 3).
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