Factor Calculator

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Prime factorization—
Number of factors—
Sum of factors—
Factor pairs—
Is it prime?—

This free factor calculator finds every factor of any whole number instantly — the full factor list, the factor pairs, the prime factorization, the sum and count of factors, and whether the number is prime.

factor calculator showing factors and prime factorization
Enter any number to see its factors and prime factorization.

How to use the factor calculator

  1. Type a whole number into the box.
  2. Press “Find factors” to see the complete list.
  3. Read the results — factor pairs, prime factorization, and whether the number is prime.

What are factors?

A factor of a number is a whole number that divides it exactly, with no remainder. Every number has at least two factors — 1 and itself. A number with exactly two factors is prime; a number with more is composite.

Prime factorization

The prime factorization expresses a number as a product of primes only, for example $60 = 2^2 \times 3 \times 5$. By the fundamental theorem of arithmetic this breakdown is unique, and it is the fastest route to the greatest common factor (GCF) and least common multiple (LCM) of two numbers.

💡 Shortcut To find all factors quickly, you only need to test divisors up to the square root of the number — each one pairs with a matching larger factor.

Popular factor lookups

Jump to a worked page: Factors of 30 Factors of 36 Factors of 24 Factors of 48 Factors of 40 Factors of 72 Factors of 60 Factors of 12 Factors of 45 Factors of 20 Factors of 16 Factors of 100 Factors of 64 Factors of 50. Related idea: exponents and their inverse, the logarithm. Formal reference: divisors on Wikipedia.

Frequently asked questions

What is a factor calculator?
A factor calculator finds every whole number that divides your number exactly. Enter any number and it returns all its factors, the factor pairs, the prime factorization, the sum and count of factors, and whether the number is prime.
What are factors?
Factors of a number are the whole numbers that divide it with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.
What is prime factorization?
Prime factorization writes a number as a product of prime numbers only, such as 12 = 2^2 x 3. It is unique to each number by the fundamental theorem of arithmetic.
What is a factor pair?
A factor pair is two numbers that multiply to give the original number. For 12 the factor pairs are (1, 12), (2, 6) and (3, 4).
How do you find the factors of a number?
Test each whole number from 1 up to the square root of your number; if it divides evenly it is a factor, and it pairs with a matching larger factor. The calculator does this instantly.
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