Prime Factorization Calculator
Enter a whole number to get its prime factors in exponent form, with every trial-division step shown.
Reviewed by the OmniCalc teamMethod verified 2026-07-01
Whole number from 2 to 1,000,000,000,000
2² × 3 × 5
= 2 × 2 × 3 × 5
Prime factorization of 60: 2² × 3 × 5Show steps
- Start with n = 60. Divide by 2 first, then by odd numbers up to √n, dividing each prime out completely.
- 60 ÷ 2 = 30 — 2 is a prime factor.
- 30 ÷ 2 = 15 — 2 is a prime factor.
- 15 ÷ 3 = 5 — 3 is a prime factor.
- 5 ÷ 5 = 1 — the remaining 5 is a prime number (no smaller prime divides it).
- Group repeated primes as exponents: 60 = 2² × 3 × 5.
How to use the prime factorization calculator
- 1Type a whole number from 2 to 1,000,000,000,000 (for example 60).
- 2Read the factorization in exponent form — 2² × 3 × 5 — with the expanded product underneath.
- 3Open Show steps to see every division; if the number is prime, the calculator says so outright.
What the exponents tell you
When every exponent is even, the number is a perfect square — 36 = 2² × 3². Shared prime factors are also how the GCF of two numbers is built, so it’s worth trying the GCF & LCM calculator to see that in action.
Frequently asked questions
What is prime factorization?
Every whole number greater than 1 is either prime or a product of primes in exactly one way — the fundamental theorem of arithmetic. Prime factorization finds that product, for example 60 = 2² × 3 × 5.
How does the calculator find the factors?
By trial division: it divides out 2 as many times as possible, then tries the odd numbers 3, 5, 7… up to the square root of what remains. Anything left over greater than 1 is itself a prime factor.
What do the small raised numbers mean?
They are exponents — how many times a prime repeats. 2³ means 2 × 2 × 2, so 1000 = 2³ × 5³ says 1000 is three 2s and three 5s multiplied together.
What is prime factorization used for?
Reducing fractions, finding the GCF and LCM of two numbers, spotting perfect squares (every exponent is even) and cryptography — RSA security rests on how hard it is to factor huge numbers.