Factors of 100
Every whole number that divides 100 exactly, the factor pairs, and how to find them yourself.
The answer
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Factor pairs of 100
| Pair | Makes |
|---|---|
| 1 × 100 | 100 |
| 2 × 50 | 100 |
| 4 × 25 | 100 |
| 5 × 20 | 100 |
| 10 × 10 | 100 |
10 × 10 uses the same number twice, so 10 counts once. That is why 100 has an odd number of factors: 9.
Prime factors of 100
- Prime factorisation
- 100 = 2 × 2 × 5 × 5 (2² × 5²)
- Is 100 prime?
- No. It has 9 factors, not just 1 and 100.
- Is 100 a square number?
- Yes. 10 × 10 = 100.
How to find the factors of 100
100 is even, so 2 is sure to be a factor. It ends in 0, so 5 is a factor. It is a square number, so one pair is 10 × 10, the same number twice. Work up from 1 to 10, and write down both numbers in every pair you find.
- 100 ÷ 1 = 100, so 1 × 100 is a pair.
- 100 ÷ 2 = 50, so 2 × 50 is a pair.
- 3 does not go into 100 exactly.
- 100 ÷ 4 = 25, so 4 × 25 is a pair.
- 100 ÷ 5 = 20, so 5 × 20 is a pair.
- 6 does not go into 100 exactly.
- 7 does not go into 100 exactly.
- 8 does not go into 100 exactly.
- 9 does not go into 100 exactly.
- 100 ÷ 10 = 10, so 10 × 10 is a pair.
Stop at 11: 11 × 11 = 121, which is more than 100. The next pair you would find is 20 × 5, which is 5 × 20 turned round, so you already have every pair.
100 in the times tables
4 × 25 = 100, 5 × 20 = 100 and 10 × 10 = 100. Practise the 10 times table, 20 times table and 25 times table.
More numbers
Check whether 100 is prime or see the square root of 100.
Questions parents ask
What is the largest factor of 100, apart from 100 itself?
50. Divide 100 by its smallest factor above 1, which is 2: 100 ÷ 2 = 50.
What do the factors of 100 add up to?
217. Leaving out 100 itself, they add up to 117, which is more than 100, so 100 is called an abundant number.
Which number after 100 has the same number of factors?
196. Like 100, 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.