Factor Calculator
Factors1, 2, 3, 4, 6, 8, 12, 24
Factor Count8
Factor Pairs(1, 24), (2, 12), (3, 8), (4, 6)
The factor calculator lists every positive divisor of a single whole number, counts how many there are, and pairs them into the factor pairs that multiply back to the original. Because a number with exactly two factors — 1 and itself — is prime, the divisor list doubles as a primality check. It is ideal for exploring a number’s structure or finding all the ways it can be split into equal groups.
Formula
factors(n) = { d : 1 ≤ d ≤ n and n mod d = 0 }; pairs: d × (n / d) = n
- n
- The positive integer being factored
- d
- A divisor — a number that divides n with no remainder
- n / d
- The complementary divisor that pairs with d to give n
How it works
- Enter one positive whole number to factor.
- The calculator tests divisors up to the square root and pairs each small divisor with its complement, producing the complete ascending list of factors efficiently.
- It shows all factors, the total factor count, and the factor pairs (such as 1×36, 2×18, 3×12) that each multiply to the original number.
Worked examples
Find all the factors of 36.
- Test divisors and pair each with its complement: 1×36, 2×18, 3×12, 4×9, 6×6.
- Collect them in order: 1, 2, 3, 4, 6, 9, 12, 18, 36.
36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36, in five factor pairs.
Factor the number 13.
- The only divisors are 1 and 13 itself.
- With exactly two factors, 13 is prime.
13 has 2 factors (1 and 13), so it is a prime number.
Frequently asked questions
- How is this different from a common factor calculator?
- This tool lists every divisor of one single number and its factor pairs. A common factor calculator instead compares two or more numbers and reports only the divisors they share.
- How can I tell if a number is prime from its factors?
- A prime number has exactly two factors: 1 and itself. If the factor count this calculator reports is 2, the number is prime.
- What is a factor pair?
- A factor pair is two divisors that multiply to give the original number, such as 4×9 = 36. Pairs are a tidy way to see all the ways a number can be split into equal-sized groups.
- What is the difference between factors and prime factors?
- Factors are all divisors of a number, while prime factors are only the prime numbers whose product equals it (for example 36 = 2×2×3×3). Use a prime factorization calculator for the latter.