Prime Factorization Calculator
Discover the prime factors as well the factor tree of any integer effortlessly with our Prime Factorization Calculator.
Prime factorisation2^3 × 3^2 × 5
Is it prime?No
Distinct primes3
Total prime factors6counting repeats
Number of divisors24
Sum of divisors1,170
Divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72…
Prime powers
| Prime | Exponent | Value |
|---|---|---|
| 2 | 3 | 8 |
| 3 | 2 | 9 |
| 5 | 1 | 5 |
The method
every integer above 1 factors into primes in exactly one way
The fundamental theorem of arithmetic
Every integer greater than 1 is either prime or factors into primes in exactly one way, ignoring order. That uniqueness is what makes prime factorisation useful: it is a fingerprint for the number, and GCDs, LCMs and divisor counts all fall straight out of it.
The divisor count comes from adding one to each exponent and multiplying: 360 = 2³·3²·5 has (3+1)(2+1)(1+1) = 24 divisors.