Factor Calculator
Enter a whole number to list all of its factors in order, along with the factor pairs that multiply to it, how many factors it has, their sum and its prime factorization. It works for any number up to one trillion and tells you straight away whether the number is prime.
- Number of factors
- 12
- Factor pairs
- 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10
- Prime factorization
- 2² × 3 × 5
- Prime or composite
- Composite
- Sum of all factors
- 168
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Formula
How to use it
- Enter a whole number from 1 to 1,000,000,000,000.
- Read the full list of factors, smallest to largest.
- Use the factor pairs when you need two numbers that multiply to it, such as the sides of a rectangle with a given area.
Worked examples
Factors of 60
- Factors
- 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Number of factors
- 12
- Factor pairs
- 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10
- Prime factorization
- 2² × 3 × 5
- Prime or composite
- Composite
- Sum of all factors
- 168
Factors of 36, a perfect square
- Factors
- 1, 2, 3, 4, 6, 9, 12, 18, 36
- Number of factors
- 9
- Factor pairs
- 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
- Prime factorization
- 2² × 3²
- Sum of all factors
- 91
Factors of 97
- Factors
- 1, 97
- Number of factors
- 2
- Factor pairs
- 1 × 97
- Prime or composite
- Prime
Factors of 100
- Factors
- 1, 2, 4, 5, 10, 20, 25, 50, 100
- Number of factors
- 9
- Prime factorization
- 2² × 5²
- Sum of all factors
- 217
How the factors are found
Try each number from 1 up to the square root of n. Whenever one divides evenly, both it and n divided by it are factors. The square root of 60 is about 7.75, so you only need to test 1 to 7, which gives 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12 and 6 × 10: twelve factors in all.
A perfect square has an odd number of factors, because its middle pair is one number twice: 36 = 6 × 6, so 36 has 9 factors rather than 10.
Factors, multiples and prime factors
Factors divide into a number; multiples are what you get by multiplying it. 12 is a factor of 60, and 60 is a multiple of 12.
The prime factorization describes every factor at once. 60 = 2² × 3 × 5, and each factor of 60 is 2 to the power 0, 1 or 2, times 3 to the power 0 or 1, times 5 to the power 0 or 1. That is (2 + 1) × (1 + 1) × (1 + 1) = 12 choices, so 12 factors.
Questions people ask
What are the factors of 24?
1, 2, 3, 4, 6, 8, 12 and 24: eight factors, in the pairs 1 × 24, 2 × 12, 3 × 8 and 4 × 6.
What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18 and 36. That is nine factors, because the pair 6 × 6 counts once.
What are the factors of 100?
1, 2, 4, 5, 10, 20, 25, 50 and 100.
Is 1 a factor of every number?
Yes. 1 and the number itself are always factors. A number whose only factors are those two is prime; 1 itself is neither prime nor composite.