Factors of 36
Every whole number that divides 36 exactly, the factor pairs, and how to find them yourself.
The answer
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Factor pairs of 36
| Pair | Makes |
|---|---|
| 1 × 36 | 36 |
| 2 × 18 | 36 |
| 3 × 12 | 36 |
| 4 × 9 | 36 |
| 6 × 6 | 36 |
6 × 6 uses the same number twice, so 6 counts once. That is why 36 has an odd number of factors: 9.
Prime factors of 36
- Prime factorisation
- 36 = 2 × 2 × 3 × 3 (2² × 3²)
- Is 36 prime?
- No. It has 9 factors, not just 1 and 36.
- Is 36 a square number?
- Yes. 6 × 6 = 36.
How to find the factors of 36
36 is even, so 2 is sure to be a factor. Its digits add up to 9, a multiple of 9, so 3 and 9 are factors. It is a square number, so one pair is 6 × 6, the same number twice. Work up from 1 to 6, and write down both numbers in every pair you find.
- 36 ÷ 1 = 36, so 1 × 36 is a pair.
- 36 ÷ 2 = 18, so 2 × 18 is a pair.
- 36 ÷ 3 = 12, so 3 × 12 is a pair.
- 36 ÷ 4 = 9, so 4 × 9 is a pair.
- 5 does not go into 36 exactly.
- 36 ÷ 6 = 6, so 6 × 6 is a pair.
Stop at 7: 7 × 7 = 49, which is more than 36. The next pair you would find is 9 × 4, which is 4 × 9 turned round, so you already have every pair.
36 in the times tables
2 × 18 = 36, 3 × 12 = 36, 4 × 9 = 36 and 6 × 6 = 36. Practise the 3 times table, 4 times table, 6 times table, 9 times table, 12 times table and 18 times table.
More numbers
Check whether 36 is prime or see the square root of 36.
Questions parents ask
What is the largest factor of 36, apart from 36 itself?
18. Divide 36 by its smallest factor above 1, which is 2: 36 ÷ 2 = 18.
What do the factors of 36 add up to?
91. Leaving out 36 itself, they add up to 55, which is more than 36, so 36 is called an abundant number.
Which number after 36 has the same number of factors?
100. Like 36, it has exactly 9 factors.
Number facts are the base of 11+ maths
Factors, multiples, primes and square numbers come up all over 11+ maths, from simplifying fractions to ratio. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.