How to find the prime factorization
- Type a whole number, such as 360.
- The prime factorization appears in exponent form (2³ × 3² × 5), with whether the number is prime, its divisor count and the nearest primes.
- Open "All divisors" to see every number that divides it evenly.
Factor trees and repeated division
To factor by hand, divide by the smallest prime that goes in evenly and repeat with the quotient: 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, and 5 is prime. Collect the primes: 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5. A factor tree is the same process drawn as branches. You only need to test primes up to the square root of what is left; if none divides it, the remainder is prime.
The exponents tell you how many divisors a number has: add one to each exponent and multiply. 360 = 2³ × 3² × 5¹ has (3+1)(2+1)(1+1) = 24 divisors. Prime factorization is used to simplify fractions and roots (√360 = 6√10), to find GCF and LCM, and it underpins RSA encryption, which relies on how hard it is to factor products of two very large primes.
FAQ
What is the prime factorization of 100?
2² × 5².
Is every number a product of primes?
Yes. Every whole number above 1 is either prime or a unique product of primes (the fundamental theorem of arithmetic).
How large a number can it factor?
Up to 9,007,199,254,740,991. Numbers with two large prime factors may take a second.