How this calculator works
Every whole number above 1 is either prime or a unique product of primes (the fundamental theorem of arithmetic).
The calculator divides by 2, then by odd numbers, up to the square root of what remains. Whatever is left above 1 is also prime.
Exponent form groups repeated primes: 2 × 2 × 2 = 2³.
The number of divisors is found by adding 1 to each exponent and multiplying: 360 = 2³ × 3² × 5 has 4 × 3 × 2 = 24 divisors.
Worked example
360
- 360 ÷ 2 ÷ 2 ÷ 2 = 45; 45 ÷ 3 ÷ 3 = 5; 5 is prime.
- Prime factorization: 2³ × 3² × 5.
- Divisors: 24.
Questions people ask
Is 1 a prime number?
No. A prime has exactly two divisors, 1 and itself; 1 has only one.
What is the smallest prime?
2, which is also the only even prime.
Why does prime factorization matter?
It is the basis for simplifying fractions, finding GCF and LCM, and, at a much larger scale, the RSA encryption that protects online payments, which relies on how hard it is to factor huge numbers.
How can I tell quickly if a number is divisible by 3?
Add its digits: if the sum is divisible by 3, so is the number. 360 has digits summing to 9, so it divides by 3.
Last reviewed October 2, 2026