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Math Prime Factors Calculator

Enter an integer greater than 1.

How this prime factors calculator works

Enter a whole number greater than 1. The calculator repeatedly divides that number by the smallest integer that goes evenly into the remaining value, starting at 2, and collects every successful divisor. Those divisors are the prime factors. For 12 the list is 2 × 2 × 3, because 12 ÷ 2 = 6, 6 ÷ 2 = 3, and 3 is prime.

Prime factorization writes a number as a product of primes only. 60 becomes 2 × 2 × 3 × 5. 100 becomes 2 × 2 × 5 × 5. 8 becomes 2 × 2 × 2. Repeated primes appear once for each time they divide. Multiplying every term recovers the original integer.

A prime number has only itself in the list. 7 shows 7. 97 shows 97. The smallest accepted input is 2, which also shows 2. Values of 1, 0, negatives, decimals, or an empty field are rejected with “Enter an integer greater than 1.”

This is not a full factor list. Factors of 12 include 1, 2, 3, 4, 6, and 12. This page shows only the primes that multiply to the number, joined with ×, in the order trial division finds them.

Prime factorization examples

Each row matches the calculator: the product of the listed primes equals the number.

NumberPrime factorsWhat it marks
122 × 2 × 312 = 2 × 2 × 3
602 × 2 × 3 × 5Common textbook example
842 × 2 × 3 × 7Two factors of 2
1002 × 2 × 5 × 5Squares of 2 and 5
82 × 2 × 2Power of a single prime
77Already prime
9797Larger prime
22Smallest allowed input

How to read the result

  • Product of primes

    2 × 2 × 3 × 5 multiplies back to 60.

  • Repeated primes stay

    100 is 2 × 2 × 5 × 5, not 2 × 5.

  • Primes stay as themselves

    7 and 97 each show a single term.

  • Integer greater than 1

    1, 0, negatives, and decimals are rejected.

Frequently asked questions

  • What does this prime factors calculator show?

    The prime factorization of an integer greater than 1. Each factor is a prime, and when you multiply them all you get the original number. For 12 the list is 2 × 2 × 3. For 60 it is 2 × 2 × 3 × 5.

  • How are the factors found?

    The page divides the number by 2 as many times as it goes evenly, then by 3, then by 4, and so on, collecting every divisor that divides the remaining value. Because larger composites are already broken by smaller primes, every collected digit is prime. For 84 the result is 2 × 2 × 3 × 7.

  • What numbers are accepted?

    Only whole numbers greater than 1. The placeholder says “Enter integer > 1.” Values such as 1, 0, a negative, a decimal, or an empty field show “Enter an integer greater than 1.” and no list.

  • What if I enter a prime number?

    A prime has only itself as a prime factor. 7 shows 7. 97 shows 97. The product of that single term is still the number you entered.

  • Why does 12 show 2 × 2 × 3 instead of 2 × 6?

    6 is not prime. The calculator keeps dividing by the smallest working divisor until only primes remain. 12 ÷ 2 = 6, 6 ÷ 2 = 3, and 3 is prime, so the full factorization is 2 × 2 × 3.

  • Are repeated primes listed separately?

    Yes. Each time the same prime divides the remaining value, it appears again. 100 is 2 × 2 × 5 × 5, not 2 × 5. 8 is 2 × 2 × 2.

  • Is this the same as listing all factors?

    No. All factors of 12 include 1, 2, 3, 4, 6, and 12. Prime factors are only the primes that multiply to 12: 2, 2, and 3. This page shows that prime product, joined with ×.

  • Does the order of factors matter?

    The page lists factors in ascending order as trial division finds them, starting from 2. 60 always appears as 2 × 2 × 3 × 5. Multiplying in any order still equals 60.

  • What is the smallest number I can enter?

    2. It is the smallest integer greater than 1 and is itself prime, so the result is 2. 1 and everything below it are rejected.

  • How do I check the answer?

    Multiply the listed primes. 2 × 2 × 3 × 5 = 60. 2 × 2 × 5 × 5 = 100. If the product matches the number you typed, the factorization is complete.