Math
Prime Factorization Calculator
Check whether a number is prime, break it into prime factors, and count its divisors.
Is 360 prime?
No
- Prime factors
- 2³ × 3² × 5
- Number of divisors
- 24
360 = 2³ × 3² × 5, so it has 24 divisors.
How it's worked out
- Divide by each prime in turn
2, 3, 5, 7 … up to √n2³ × 3² × 5 - Count the divisors
(3 + 1) × (2 + 1) × (1 + 1)24
How it works
The number is divided by 2, then 3, then each possible prime up to its square root. Whatever is left above 1 is itself prime.
Worked example
360 ÷ 2 ÷ 2 ÷ 2 = 45, 45 ÷ 3 ÷ 3 = 5, and 5 is prime. So 360 = 2³ × 3² × 5, with 24 divisors.
Questions people ask
What is prime factorization?
Writing a number as a product of primes. 360 = 2³ × 3² × 5.
How do I count a number's divisors?
Add 1 to each exponent in the prime factorization and multiply. For 360: (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors.
Is 1 a prime number?
No. A prime has exactly two divisors, 1 and itself, so the smallest prime is 2.
About this calculator
Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem