The factors (or divisors) of a number are the whole numbers that divide it exactly, with no remainder. They come in factor pairs that multiply to the number. This calculator lists every factor and pair, counts and sums them, and tells you whether the number is prime or a perfect square.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: exact divisor enumeration, recomputed in code.
How factors are found
You only need to test divisors up to the square root, because factors come in pairs straddling it — one below √n and its partner above. A number with an odd count of factors is a perfect square, since its square root pairs with itself. A number with exactly two factors (1 and itself) is prime.
Worked examples
24:
36 (perfect square):
13 (prime):
The sum of the factors of 24 is 60, and of 36 is 91. Factor lists like these are the foundation for simplifying fractions, computing the greatest common divisor and least common multiple, and prime factorization.
Frequently Asked Questions
Whole numbers that divide it exactly. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Two factors that multiply to the number. For 24: 1×24, 2×12, 3×8, 4×6.
Varies — primes have 2, 24 has 8, 36 has 9. Perfect squares have an odd count.
Test divisors up to √n; each gives a pair (d and n÷d).
No — factors are all divisors; prime factors are only the prime ones. 12 → factors 1,2,3,4,6,12; primes 2×2×3.