How it is calculated
- Divide the number by 2 as many times as possible, then by 3, 5, 7 and the next odd numbers, up to the square root of what is left
- Each divisor that works is a prime factor, and the number of times it divides is its exponent
- Anything greater than 1 left over at the end is also prime
- Number of divisors = (exponent 1 + 1) × (exponent 2 + 1) × …
To test one number, use the prime number calculator. To find common factors of several numbers, use the GCF calculator.
Worked example
360:
- 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, so 2 divides it 3 times
- 45 ÷ 3 = 15, ÷ 3 = 5, so 3 divides it 2 times
- 5 is prime
- 360 = 2³ × 3² × 5, which has 4 × 3 × 2 = 24 divisors
Why your number may differ
The calculator accepts whole numbers up to one trillion. Very large numbers with two large prime factors take longer to factor.