Factor Calculator

Enter a whole number to list all of its factors, its factor pairs and its prime factorization. Works for numbers up to 1,000,000,000,000.

How to use the factor calculator

Type a whole number and the factors appear instantly. You also get the factor pairs, the prime factorization in exponent form, the number of factors and whether the number is prime.

What is a factor?

A factor of a number divides it exactly, with no remainder. 6 is a factor of 24 because 24 ÷ 6 = 4. Factors always come in pairs that multiply to the original number: 1 × 24, 2 × 12, 3 × 8 and 4 × 6.

How to find all factors of a number

Start at 1 and test each whole number to see if it divides your number exactly.
Each time you find a factor, write down its partner (the number ÷ factor) as well.
Stop when the number you are testing is larger than the square root of your number. After that point you would only find partners you already have.

For 360, you only need to test up to √360 ≈ 18.97, so 18 tests find all 24 factors.

Prime factorization

Prime factorization writes a number as a product of prime numbers. It is unique for every number above 1. For 360: 360 = 2 × 180 = 2 × 2 × 90 = … = 2³ × 3² × 5.

Number of factors = (a + 1)(b + 1)(c + 1)… for n = p₁ᵃ × p₂ᵇ × p₃ᶜ …

For 360 = 2³ × 3² × 5¹ that gives (3+1)(2+1)(1+1) = 24 factors, which matches the list.

Factors of common numbers

Number	Factors	Prime factorization
12	1, 2, 3, 4, 6, 12	2² × 3
24	1, 2, 3, 4, 6, 8, 12, 24	2³ × 3
36	1, 2, 3, 4, 6, 9, 12, 18, 36	2² × 3²
48	1, 2, 3, 4, 6, 8, 12, 16, 24, 48	2⁴ × 3
60	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	2² × 3 × 5
100	1, 2, 4, 5, 10, 20, 25, 50, 100	2² × 5²

Frequently asked questions

What are the factors of a number?

They are the whole numbers that divide it exactly. For example, the factors of 18 are 1, 2, 3, 6, 9 and 18.

How do I know if a number is prime?

A prime number has exactly two factors: 1 and itself. The calculator labels the number as prime or composite for you.

Is 1 a prime number?

No. 1 has only one factor, so it is neither prime nor composite.

Do negative numbers have factors?

Yes. Every positive factor has a negative partner too, so −3 × −8 = 24. The calculator lists the positive factors and notes the negatives.

What is the difference between factors and multiples?

Factors divide into a number, so they are equal to or smaller than it. Multiples are the number times 1, 2, 3 and so on, so they are equal to or larger than it.

Does this factor polynomials?

This page factors whole numbers. Use the polynomial calculator for expressions such as x² + 5x + 6.