Prime Factorization Calculator

Break any whole number (up to 18 digits) into its prime factors, shown in exponent form with a factor tree and divisor count.

Enter values

Result

Prime factorization

2^3 × 3^2 × 5

Expanded: 2 × 2 × 2 × 3 × 3 × 5
Distinct primes: 3
Number of divisors: 24

Step-by-stepShow

360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

About the Prime Factorization Calculator

Break any whole number (up to 18 digits) into its prime factors, shown in exponent form with a factor tree and divisor count.

Also known as: prime factors, factor tree, prime decomposition, factorise number.

How to use this calculator

Enter whole number.
The result updates instantly as you type — press Calculate (or Enter) at any time.
Open “Step-by-step” to see how the answer was worked out.
Use Copy result or Share to save the answer or send a link with your inputs.

Formula

n = p₁^a₁ × p₂^a₂ × … × pₖ^aₖ

Worked example

Using the values pre-filled in the calculator above:

Whole number: 360

the calculator returns:

Prime factorization: 2^3 × 3^2 × 5
Expanded: 2 × 2 × 2 × 3 × 3 × 5
Distinct primes: 3
Number of divisors: 24

Working

360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

Frequently asked questions

How do you find prime factors?

Divide by the smallest prime (2) as many times as possible, then 3, 5, 7 and so on until the quotient is 1. 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.