Factor Pairs Calculator
A factor pair is two whole numbers that multiply to give a number. The factor pairs of 36 are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
Enter a whole number from 1 to 100,000 to list all of its factor pairs.
Find Factor Pairs
How to find factor pairs
- Start with 1 × the number. That is always a factor pair.
- Try dividing by 2, 3, 4 and so on. Each time it divides evenly, the divisor and the answer make a pair: 36 ÷ 4 = 9, so (4, 9).
- Stop when you reach the square root (for 36, that is 6). After that the pairs just repeat in reverse order.
A number with only one factor pair (1 × itself) is prime. A square number, like 16 or 36, has one pair where both numbers are the same.
Watch a short video on factor pairs.
Worked examples
What are the factor pairs of 24?
24 ÷ 1 = 24, 24 ÷ 2 = 12, 24 ÷ 3 = 8, 24 ÷ 4 = 6. 5 doesn't divide 24, and the square root is about 4.9, so stop. Pairs: (1, 24), (2, 12), (3, 8), (4, 6).
What are the factor pairs of 40?
(1, 40), (2, 20), (4, 10), (5, 8). 3 doesn't divide 40 and 6 is past the square root (about 6.3).
What are the factor pairs of 45?
45 is odd, so 2 and 4 won't work. (1, 45), (3, 15), (5, 9).
What are the factor pairs of 16?
(1, 16), (2, 8), (4, 4). 16 is a square number, so one pair repeats the same number.
Popular factor pairs
Frequently asked questions
- Are factor pairs the same as factors?
- Factor pairs group the factors two at a time. The factors of 12 are 1, 2, 3, 4, 6 and 12; the factor pairs are (1, 12), (2, 6) and (3, 4).
- Does order matter in a factor pair?
- No. (3, 8) and (8, 3) are the same pair, which is why you can stop at the square root.
- How many factor pairs does a prime number have?
- Exactly one: 1 and the number itself. 13 has only the pair (1, 13).
- Can factor pairs be negative?
- Yes, (−4) × (−6) = 24 too, but in school and in this calculator factor pairs usually mean positive whole numbers.