How to Calculate Factors
What is Factors?
Factors (or divisors) of a number n are all integers that divide n exactly with no remainder. Prime factorization expresses n as a product of prime numbers — unique for every integer greater than 1 (Fundamental Theorem of Arithmetic).
Step-by-Step Guide
- 1Trial division: test divisibility by 2, then odd numbers up to √n
- 2If divisible, it's a factor — add both divisor and quotient
- 3Prime factorization: keep dividing by the smallest prime factor
- 4Number of factors = product of (exponent + 1) for each prime factor
Worked Examples
Input
Factors of 36
Result
1, 2, 3, 4, 6, 9, 12, 18, 36
36 = 2² × 3² → (2+1)(2+1) = 9 factors
Input
Prime factorization of 360
Result
2³ × 3² × 5
360 = 8 × 9 × 5
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