How to use the Prime Factorization Calculator
Enter a whole number up to one trillion. The result lists its prime factors with powers, such as 2³ × 3² × 5.
How to factor by hand
Keep dividing by the smallest prime that fits. 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45. Now 2 no longer divides, so try 3: 45 ÷ 3 = 15, ÷ 3 = 5. Five is prime, so you stop. That gives 360 = 2³ × 3² × 5, and every whole number above 1 has exactly one such breakdown.
What the factors tell you
Prime factors make GCD and LCM problems easy and help simplify fractions and square roots. They also count divisors: add one to each power and multiply. For 360, that is (3 + 1) × (2 + 1) × (1 + 1) = 24, so 360 has 24 divisors, one reason it works so well for the degrees in a circle.
How it works
Repeatedly divide by prime factors.
Examples
- 360
360 = 2 × 2 × 2 × 3 × 3 × 5
- 84
84 = 2 × 2 × 3 × 7
- 97, a prime number
97 = 97
Limitations and assumptions
Limited to safe integers up to 1,000,000,000,000.
Frequently asked questions
What is prime factorization?
Writing a number as a product of primes; every integer above 1 has exactly one such form.
How do I do it by hand?
Divide by 2 until you can no longer, then by 3, then 5 and so on.
What if the number is prime?
The result is the number itself.
Why does it matter?
It helps simplify fractions and underpins cryptography.