Factor Calculator
Enter a whole number to list every factor, the pairs that multiply to give it, and its breakdown into prime factors.
Result
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
1 × 360 2 × 180 3 × 120 4 × 90 5 × 72 6 × 60 8 × 45 9 × 40 10 × 36 12 × 30 15 × 24 18 × 20
- Prime or composite
- Composite
- Sum of all factors
- 1,170
Formula
- f is a factor of n when n ÷ f leaves no remainder
- Factors come in pairs f and n ÷ f, so only numbers up to √n need testing
- Number of factors = (e₁ + 1) × (e₂ + 1) × … for n = p₁^e₁ × p₂^e₂ × …
How the Factor Calculator works
A factor of a number divides it exactly. Every factor below the square root pairs with one above it, which is why the calculator only tests divisors up to the square root.
The prime factorization writes the number as a product of primes. It is unique for every whole number above 1, a result known as the fundamental theorem of arithmetic.
Worked example
360 = 2³ × 3² × 5. It has (3 + 1) × (2 + 1) × (1 + 1) = 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.
Frequently asked questions
What is the difference between factors and prime factors?
Factors are all the whole numbers that divide a number. Prime factors are only those that are prime. The factors of 12 are 1, 2, 3, 4, 6 and 12, and its prime factors are 2 and 3.
Is 1 a prime number?
No. A prime has exactly two factors, 1 and itself. The number 1 has only one factor.
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