Prime Factorization
Break any whole number into its prime factors and test divisibility, with the division steps shown. Enter a number like 360 and get its factorization in exponent form.
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What you can do with the Prime Factorization
Break any number into primes and test divisibility.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. prime factorization of 360
How the Prime Factorization works
- Divide by the smallest prime (2) as many times as possible.
- Move to the next primes (3, 5, 7…) and repeat until the quotient is 1.
- Write the primes as a product using exponents: 360 = 2³ × 3² × 5.
Frequently asked questions
What is a prime number?
A prime has exactly two factors, 1 and itself. 2, 3, 5, 7 and 11 are primes; 1 is not.
How can I tell if a number is divisible by 3?
Add its digits. If the digit sum is divisible by 3, so is the number.
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Math Solver can make mistakes. Please double-check important steps and calculations.