Prime Factorization Calculator

What This Calculator Does

Every whole number is built by multiplying prime numbers together. Primes (2, 3, 5, 7, 11, and so on) are the “atoms” of arithmetic, because they cannot be broken down any further. Prime factorization finds that unique recipe of primes for a number.

For example, 12 is 2 x 2 x 3, and 360 is 2^3 x 3^2 x 5. Every number has exactly one such recipe, which is why prime factors are the key to finding a GCF or LCM and to simplifying fractions.

How Prime Factorization Works

Divide by the smallest prime that fits, repeat with the result, and continue until only prime factors remain.

For 360: $360 = 2 \times 180 = 2 \times 2 \times 90 = \dots = 2 \times 2 \times 2 \times 3 \times 3 \times 5$, written $2^3 \times 3^2 \times 5$.

How to Use It

1. Enter a whole number of 2 or more.
2. Read the prime factorization, with exponents and the expanded form.

Worked Examples

Number	Prime factorization
360	2^3 x 3^2 x 5
100	2^2 x 5^2
84	2^2 x 3 x 7
17	prime

FAQ

What is prime factorization?

Writing a number as a product of prime numbers. For 84: $2 \times 2 \times 3 \times 7$, or $2^2 \times 3 \times 7$.

What if the number is prime?

A prime number has no factors other than 1 and itself, so the tool reports that it is prime (for example, 17).

How is this used?

Prime factors are used to find the greatest common factor and least common multiple, and to simplify fractions. See the GCF and LCM calculator.