Prime Factorization Calculator
Break an integer down into its prime factors and check whether it's a prime number, with the result expressed as a product of powers (for example, 360 = 2³ × 3² × 5).
How is it calculated?
The number is repeatedly divided by the smallest possible prime (2, then 3, 5, 7, 11...) as long as it divides evenly, counting how many times it divides by each one (the exponent). The process ends when what's left is 1, or when what's left is a prime larger than the square root of the original number (that remainder is added as the last factor).
Examples
Factorize 360
360 = 2³ × 3² × 5.
Check if 97 is prime
97 is a prime number (its only factorization is 97¹).
Step-by-step example
Factoring 360: 360 ÷ 2 = 180, 180 ÷ 2 = 90, 90 ÷ 2 = 45 (no longer divisible by 2, exponent of 2 is 3). 45 ÷ 3 = 15, 15 ÷ 3 = 5 (no longer divisible by 3, exponent of 3 is 2). 5 ÷ 5 = 1 (exponent of 5 is 1). Result: 360 = 2³ × 3² × 5.