Prime Factorization Calculator guide
Prime Factorization Calculator: Prime Factors and Index Form
Use our prime factorization calculator to write any number as a product of prime factors in index form, with a division ladder.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
Every whole number above 1 is either prime or can be written as a product of primes in exactly one way. Our Prime Factorization Calculator finds those primes for you.
How to use the calculator (Prime Factorization Calculator)
Enter a whole number of 2 or more. You'll see:
- The prime factorisation in index form, such as 2³ × 3² × 5
- The primes written out in full
- Whether the number is prime
- A division ladder showing each step
How it works
Divide by the smallest prime that goes in exactly, and keep going with the result until you reach 1. The primes you divided by are the prime factors.
A worked example
With the calculator's default settings, 360:
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
So 360 = 2³ × 3² × 5.
Frequently asked questions
What's a factor tree?
Another way to show the same thing: split a number into any two factors, then keep splitting until every branch ends in a prime. You always get the same primes.
What's prime factorisation used for?
Finding the HCF and LCM, simplifying fractions and surds, and in cryptography, which relies on how hard it is to factorise huge numbers.
What are the first few primes?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29. 2 is the only even prime.
To use prime factors for the HCF or LCM, see our Greatest Common Factor Calculator and Least Common Multiple Calculator.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Prime factorizationmathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.