Factors of 72
Every whole number that divides 72 exactly, the factor pairs, and how to find them yourself.
The answer
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factor pairs of 72
| Pair | Makes |
|---|---|
| 1 × 72 | 72 |
| 2 × 36 | 72 |
| 3 × 24 | 72 |
| 4 × 18 | 72 |
| 6 × 12 | 72 |
| 8 × 9 | 72 |
Prime factors of 72
- Prime factorisation
- 72 = 2 × 2 × 2 × 3 × 3 (2³ × 3²)
- Is 72 prime?
- No. It has 12 factors, not just 1 and 72.
- Is 72 a square number?
- No. 8 × 8 = 64 and 9 × 9 = 81, so 72 falls between two square numbers.
How to find the factors of 72
72 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. Work up from 1 to 8, and write down both numbers in every pair you find.
- 72 ÷ 1 = 72, so 1 × 72 is a pair.
- 72 ÷ 2 = 36, so 2 × 36 is a pair.
- 72 ÷ 3 = 24, so 3 × 24 is a pair.
- 72 ÷ 4 = 18, so 4 × 18 is a pair.
- 5 does not go into 72 exactly.
- 72 ÷ 6 = 12, so 6 × 12 is a pair.
- 7 does not go into 72 exactly.
- 72 ÷ 8 = 9, so 8 × 9 is a pair.
Stop at 9: 9 × 9 = 81, which is more than 72. The next pair you would find is 9 × 8, which is 8 × 9 turned round, so you already have every pair.
72 in the times tables
4 × 18 = 72, 6 × 12 = 72 and 8 × 9 = 72. Practise the 6 times table, 8 times table, 9 times table, 12 times table and 18 times table.
More numbers
Check whether 72 is prime.
Questions parents ask
What is the largest factor of 72, apart from 72 itself?
36. Divide 72 by its smallest factor above 1, which is 2: 72 ÷ 2 = 36.
What do the factors of 72 add up to?
195. Leaving out 72 itself, they add up to 123, which is more than 72, so 72 is called an abundant number.
Which number after 72 has the same number of factors?
84. Like 72, it has exactly 12 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.