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Prime Factorization Calculator

Check whether a number is prime, break it into prime factors, and count its divisors.

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Is 360 prime?

No

Prime factors
2³ × 3² × 5
Number of divisors
24

360 = 2³ × 3² × 5, so it has 24 divisors.

How it's worked out

  1. Divide by each prime in turn2, 3, 5, 7 … up to √n2³ × 3² × 5
  2. Count the divisors(3 + 1) × (2 + 1) × (1 + 1)24

How it works

The number is divided by 2, then 3, then each possible prime up to its square root. Whatever is left above 1 is itself prime.

Worked example

360 ÷ 2 ÷ 2 ÷ 2 = 45, 45 ÷ 3 ÷ 3 = 5, and 5 is prime. So 360 = 2³ × 3² × 5, with 24 divisors.

Questions people ask

What is prime factorization?

Writing a number as a product of primes. 360 = 2³ × 3² × 5.

How do I count a number's divisors?

Add 1 to each exponent in the prime factorization and multiply. For 360: (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors.

Is 1 a prime number?

No. A prime has exactly two divisors, 1 and itself, so the smallest prime is 2.

Formula and rules last checked 25 October 2026Written and tested by the CalcPenguin teamReport a problem