Factor Calculator
Find all factors (divisors) of a whole number from 1 to 1,000,000,000,000, the numbers that divide it evenly. You can type a large number as 1e9. A decimal, 0, a negative number or anything above the limit gets a message.
How to use the Factor Calculator
- Enter your numbers in the Factor Calculator above.
- Press the Find Factors button to see the result.
- To try other numbers, change any value and press the button again.
The factor enumeration
For each k from 1 to √n: if n mod k = 0, both k and n/k are factors
The calculator stops at the square root because factors come in pairs. Each factor above √n is the partner of one below it.
Worked example
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The check stops at √36 = 6. Factor pairs: (1,36), (2,18), (3,12), (4,9), (6,6). Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The default, 60, has 12 factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Frequently asked questions
How is this different from prime factorization?
Factors include all divisors. Prime factorization breaks the number into its prime building blocks only. 36 has 9 factors; its prime factorization is 2² × 3².
How many factors does a number have?
If n = p₁^a₁ × p₂^a₂ × ... then the number of factors is (a₁+1)(a₂+1)... For 36 = 2²·3²: (2+1)(2+1) = 9 factors.
What's a perfect square in terms of factors?
A perfect square has an odd number of factors, because √n pairs with itself. 36 has 9 factors, and every number that is not a perfect square has an even count, such as 60 with 12.