Prime Factorization Calculator
Break a whole number into the prime numbers that multiply to give it, such as 360 = 2 x 2 x 2 x 3 x 3 x 5. Works for numbers up to 10¹⁵.
Last updated: October 2026
Prime Factors
2 x 2 x 2 x 3 x 3 x 5
Formula below · 3 sources (mathworld.wolfram.com, mathsisfun.com, khanacademy.org) · Updated Oct 2026
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About this calculator
Every whole number greater than 1 is either prime or a product of primes in exactly one way, apart from the order of the factors. This is the fundamental theorem of arithmetic. The prime factorization of 360 is 2 × 2 × 2 × 3 × 3 × 5, written in exponent form as 2³ × 3² × 5.
How the calculator finds it
It uses trial division: divide by 2 as many times as possible, then by 3, 5, 7 and so on, recording each prime every time it divides. It only needs to test divisors up to the square root of what is left, because a number with no factor up to its square root is prime. Whatever remains above 1 at the end is the last prime factor. For 360: 360 → 180 → 90 → 45 (three 2s), 45 → 15 → 5 (two 3s), and 5 is prime.
The result lists every prime with repeats, separated by x. If the answer is the number itself, the number is prime (97 gives 97). Inputs up to 10¹⁵ are accepted; much larger numbers need dedicated factoring software, and numbers below 2, decimals and negative numbers have no prime factorization in this sense.
Uses
Prime factors give the greatest common factor (multiply the shared primes at their lowest powers) and the least common multiple (every prime at its highest power), and they show how to simplify square roots: 72 = 2³ × 3², so √72 = 6√2.
Prime factorizations of some common numbers
Scroll sideways to see all columns →
| Number | Prime factors | Exponent form |
|---|---|---|
| 12 | 2 x 2 x 3 | 2² × 3 |
| 60 | 2 x 2 x 3 x 5 | 2² × 3 × 5 |
| 84 | 2 x 2 x 3 x 7 | 2² × 3 × 7 |
| 100 | 2 x 2 x 5 x 5 | 2² × 5² |
| 360 | 2 x 2 x 2 x 3 x 3 x 5 | 2³ × 3² × 5 |
| 1,001 | 7 x 11 x 13 | 7 × 11 × 13 |
How to use
Enter a whole number of 2 or more. Example 1: 360 gives 2 x 2 x 2 x 3 x 3 x 5, which is 2³ × 3² × 5. Check: 8 × 9 × 5 = 360. Example 2: 97 gives 97. It has no smaller prime factor, so 97 is prime. Example 3: 1001 gives 7 x 11 x 13.
Frequently asked questions
How do you find the prime factorization of a number?
Divide by the smallest prime that goes in evenly, write it down, and repeat with the quotient until you reach 1. For 84: 84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7, and 7 is prime, so 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7.
How do I write the answer in exponent form?
Count how many times each prime appears and use that count as the exponent. 2 x 2 x 2 x 3 x 3 x 5 has three 2s and two 3s, so it is 2³ × 3² × 5.
How does prime factorization give the GCF and LCM?
Factor both numbers. The GCF multiplies the primes they share, each at the lower power; the LCM multiplies every prime that appears, each at the higher power. 60 = 2² × 3 × 5 and 84 = 2² × 3 × 7, so GCF = 2² × 3 = 12 and LCM = 2² × 3 × 5 × 7 = 420.
Is 1 a prime number?
No. A prime has exactly two positive divisors, 1 and itself, and 1 has only one. Leaving 1 out is what makes every factorization unique.
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Sources & references
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