Factors Calculator
Every factor of a whole number, in pairs, with the prime factorization, how many there are, what they add to — and the factors it shares with a second number.
A factor divides the number exactly, leaving no remainder.
How the factors calculator works
A factor divides the number exactly, leaving no remainder. Factors come in pairs that multiply to the number (36 = 1×36 = 2×18 = 3×12 = 4×9 = 6×6), so testing divisors only up to the square root finds them all. The prime factorization breaks the number into primes; the number of factors is found by adding one to each prime exponent and multiplying. Comparing the two lists gives the common factors, the largest of which is the greatest common divisor.
Formula: if n = p₁^a · p₂^b … then the factor count = (a+1)(b+1)…
Worked examples
| Inputs | Number of factors | Note |
|---|---|---|
| Factors of 36 | 9 | 9 factors; shares 1, 2, 3, 4, 6, 12 with 48 |
| Factors of 28 | 6 | a perfect number — 1+2+4+7+14 = 28 |
| Factors of 97 | 2 | prime — only 1 and itself |
FAQFrequently asked questions
What is a factor?
A whole number that divides another exactly. 6 is a factor of 36 because 36 ÷ 6 = 6 with nothing left over.
What is the difference between factors and prime factors?
The factor list is every divisor; the prime factorization is the unique set of primes that multiply to the number — 36 = 2² × 3².
What is a perfect number?
One whose factors other than itself add up to itself: 6 = 1+2+3, and 28 = 1+2+4+7+14. They are rare.
How do I find the greatest common factor?
Enter a second number; the largest number in both factor lists is the GCF, shown on its own row.
Why is a prime number only two factors?
By definition a prime is divisible only by 1 and itself.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.