Prime Factorization
Break a whole number into the prime numbers that multiply to make it, such as 360 = 2^3 × 3^2 × 5. Students use prime factors to simplify fractions and to find the greatest common divisor or least common multiple by hand.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
360
360 = 2^3 × 3^2 × 5
How to use the prime factorization
- Type a whole number from 2 through 1,000,000,000,000 in the box, such as 360.
- Leave out commas and decimal points. Type 1000000, not 1,000,000.
- Press Run to see the number written as a product of primes.
- Press Copy result or Download to save it.
How it works
Factors are listed from smallest to largest. A prime that appears more than once gets an exponent, such as 2^3 for 2 × 2 × 2.
If the number is prime, the result is just the number itself, such as 97 = 97.
The tool uses trial division. It divides out 2, then tries odd numbers up to the square root of what is left.
Numbers below 2 or above one trillion, decimals, and numbers with commas are rejected with an error.
Calculations use exact big integers, so large inputs never lose precision.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
What is prime factorization?
It is writing a number as a product of prime numbers. Every whole number above 1 has exactly one prime factorization, apart from the order of the factors.
What is the prime factorization of 360?
360 = 2 × 2 × 2 × 3 × 3 × 5, written with exponents as 2^3 × 3^2 × 5.
Why does the tool start at 2?
1 is not a prime number and has no prime factors, so the smallest number you can factor is 2.
How do prime factors help with GCD and LCM?
The GCD multiplies the primes the numbers share, using the smaller power of each. The LCM uses every prime that appears, with its largest power.