Prime Factorization Calculator

By the fundamental theorem of arithmetic, every integer greater than 1 has exactly one prime factorization (apart from order). The number of divisors equals the product of each exponent plus one — for 2³ × 3² × 5 that is (3+1)(2+1)(1+1) = 24. A number with a single prime factor and exponent 1 is prime.

Divide the number by the smallest prime that fits, repeat with the quotient, and continue until you reach 1. The primes collected, with their exponents, are the factorization.

360 factors as 2 × 2 × 2 × 3 × 3 × 5, written 2³ × 3² × 5, and has 24 divisors.

1. Enter a whole number of 2 or more.
2. Press Factor.
3. Read the prime factorization and divisor count.

• Including 1 as a prime factor — 1 is not prime.
• Stopping before fully factoring a composite factor.
• Entering a decimal; only whole numbers can be factored.

The Prime Factorization Calculator breaks a whole number into the prime numbers that multiply to make it. It shows the factorization in exponent form, counts the divisors and tells you whether the number is prime.

Students, teachers and anyone working with factors, fractions or number theory.

• Prime factorization in clear exponent form.
• Counts distinct primes and total divisors.
• Flags prime numbers.
• Private — calculated entirely in your browser.

• Simplifying fractions or finding common factors.
• Working out the greatest common divisor or LCM.
• Checking number-theory homework.