The Prime Factorization Calculator breaks a whole number into its prime factors and tells you whether it is prime.
100 = 2^2 × 5^2
| Prime factorization | 2^2 × 5^2 |
| Expanded | 2 × 2 × 5 × 5 |
| Prime? | No, it is composite |
Every whole number greater than 1 is either prime or can be written as a product of primes in exactly one way (the fundamental theorem of arithmetic). 100 = 2 × 2 × 5 × 5 = 2² × 5².
Divide by the smallest prime that goes in (2, then 3, 5, 7, 11, …) and repeat with the result until you reach 1. A factor tree shows the same process visually. You only need to test primes up to the square root of the number.
Prime factorizations give the GCF and LCM, simplify fractions and roots, count divisors, and underpin public-key cryptography such as RSA, whose security relies on how hard it is to factor very large numbers.
Is 2 prime? Yes, the only even prime.
What is a composite number? A whole number above 1 that is not prime.
How large can the number be? Up to about 10¹⁵ here.