Prime Factorization Calculator

⚔ Find prime factors of any number instantly. See step-by-step division method. 100% free.

The Best Prime Factorization Calculator

Our prime factorization calculator is designed for students who want to actually understand math. We show you the complete division method step-by-step, so you actually LEARN - not just get answers. Every positive integer greater than 1 can be expressed as a unique product of prime numbers (Fundamental Theorem of Arithmetic). No signup, no ads, just instant accurate results.

Prime Factorization

n = p₁^a₁ Ɨ pā‚‚^aā‚‚ Ɨ ... Ɨ pā‚–^aā‚–

Every integer is a unique product of prime powers

Factor Tree Method

Divide by smallest prime until 1

Keep dividing by 2, 3, 5, 7, 11...

Examples

Prime Factorization of 60

160 Ć· 2 = 30
230 Ć· 2 = 15
315 Ć· 3 = 5
45 Ć· 5 = 1
560 = 2² Ɨ 3 Ɨ 5

Prime Factorization of 84

184 Ć· 2 = 42
242 Ć· 2 = 21
321 Ć· 3 = 7
47 Ć· 7 = 1
584 = 2² Ɨ 3 Ɨ 7

Frequently Asked Questions

Is this prime factorization calculator free?

Yes! 100% free with no signup required and no ads.

What is a prime number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13...

Why is 1 not a prime number?

By definition, prime numbers must have exactly two distinct factors. The number 1 only has one factor (itself), so it is not considered prime.