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).
All 12 practice questions
What are the factors of 10?
- 1, 10
- 1, 2, 4, 5, 10
- 2, 5
- 1, 2, 5, 10
Show the answer to question 1
Answer: 1, 2, 5, 10
1×10=10, 2×5=10 — so the factors of 10 are 1, 2, 5 and 10.
What are the first four multiples of 7?
- 7, 14, 20, 27
- 1, 7, 14, 21
- 7, 17, 27, 37
- 7, 14, 21, 28
Show the answer to question 2
Answer: 7, 14, 21, 28
7×1=7, 7×2=14, 7×3=21, 7×4=28.
Is 6 a factor of 24?
- Yes, because 24 ÷ 6 = 4 exactly
- No, because 24 is bigger than 6
- No, 6 doesn't divide evenly into 24
- Yes, because 6 is an even number
Show the answer to question 3
Answer: Yes, because 24 ÷ 6 = 4 exactly
24 ÷ 6 = 4 with no remainder, so 6 is a factor of 24.
Is 45 divisible by 5?
- Yes, because it ends in 5
- No, because 45 is odd
- No, 5 does not divide into 45
- Yes, because 4+5=9
Show the answer to question 4
Answer: Yes, because it ends in 5
Any number ending in 0 or 5 is divisible by 5. 45 ÷ 5 = 9 exactly.
Which of these is a factor of 20?
- 6
- 4
- 9
- 3
Show the answer to question 5
Answer: 4
20 ÷ 4 = 5 exactly, so 4 is a factor. 20 is not evenly divisible by 3, 6, or 9.
Which of these is a multiple of 9?
- 30
- 35
- 27
- 40
Show the answer to question 6
Answer: 27
9 × 3 = 27, so 27 is a multiple of 9. The others are not evenly divisible by 9.
Write 12 as a product of two factors.
- 4 × 4
- 3 × 4
- 3 × 5
- 2 × 5
Show the answer to question 7
Answer: 3 × 4
3 × 4 = 12. (2 × 6 also works, but only one option here equals 12.)
Is 17 divisible by 2?
- No, because 17 is a factor of 34
- Yes, because 17 is a small number
- No, because it's an odd number
- Yes, 17 ÷ 2 = 8 exactly
Show the answer to question 8
Answer: No, because it's an odd number
Divisible-by-2 numbers are even (end in 0,2,4,6,8). 17 is odd, so it is not divisible by 2 — 17 ÷ 2 = 8 remainder 1.
Which number is divisible by 10?
- 115
- 105
- 155
- 150
Show the answer to question 9
Answer: 150
Numbers divisible by 10 end in 0. Only 150 ends in 0.
True or false: every multiple of 8 is also a multiple of 4.
- True
- False
Show the answer to question 10
Answer: True
Since 8 = 4 × 2, any multiple of 8 (like 16 = 8×2 = 4×4) is automatically a multiple of 4 too.
What is the smallest factor any whole number (other than 0) always has?
- 1
- 0
- 2
- Itself
Show the answer to question 11
Answer: 1
Every whole number is divisible by 1, so 1 is always a factor — the smallest one.
Is 30 a multiple of 6?
- Yes, 6 × 5 = 30
- Yes, because 30 is even
- No, 30 is too big
- No, 6 is not a factor of 5
Show the answer to question 12
Answer: Yes, 6 × 5 = 30
6 × 5 = 30 exactly, so 30 is a multiple of 6 (and 6 is a factor of 30).
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