What this calculator does
A divisor of a whole number is any smaller (or equal) whole number that divides into it with nothing left over. This divisor calculator takes any positive whole number and lists every one of its divisors, from 1 up to the number itself, along with how many there are and what they add up to.
This is a different question from finding a prime factorisation, which breaks a number down into the prime numbers that multiply together to make it, or from finding a greatest common divisor, which needs two numbers to compare. Listing all the divisors of one number on its own, including the composite ones like 4, 6, 9 or 12, is its own everyday task, useful for anything from splitting a quantity into equal groups to checking whether a number is prime.
The formula
The calculator checks every whole number i from 1 up to the square root of your number n. Whenever i divides evenly into n (n mod i = 0), both i and its pairing n ÷ i are divisors. Checking only up to the square root, rather than every number up to n itself, is what keeps this fast even for large numbers, since divisors always pair up around the square root.
| Term | Meaning |
|---|---|
| Divisor | A whole number that divides another number exactly, leaving no remainder. |
| Proper divisor | A divisor of a number that is smaller than the number itself, so every divisor except the number itself. |
| Prime number | A number with exactly two divisors: 1 and itself. |
The inputs explained
| Field | What to enter |
|---|---|
| Whole number | The whole number you want the divisors of. Negative numbers use their absolute value, since divisibility does not depend on sign. |
When to use it
Splitting something into equal groups
If you have 36 items and want to know every way to split them into equal rows or boxes with none left over, the divisors of 36 give every valid group size at once.
Checking whether a number is prime
A number is prime exactly when it has only two divisors, 1 and itself. Listing the divisors settles the question directly, rather than trial-dividing by hand.
Simplifying fractions or ratios by hand
Knowing the full divisor list of the numerator or denominator makes it easy to spot the largest number that divides both, without reaching for a separate greatest-common-divisor tool.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What are the divisors of 12, 24, 36 and other common numbers?
A range of everyday numbers and their full divisor lists.
| Number | Divisors | Number of divisors |
|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 6 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 8 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 9 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 12 |
| 100 | 1, 2, 4, 5, 10, 20, 25, 50, 100 | 9 |
| 144 | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 | 15 |
Which small numbers are prime, and which have the most divisors?
A short run of numbers, showing how divisor counts jump around even between neighbours.
Questions
What is the difference between a divisor and a factor?
None in ordinary use: "divisor" and "factor" both mean a whole number that divides another exactly. Some textbooks use "factor" specifically for prime factors and "divisor" for the full list, but this calculator treats them the same and lists every divisor, prime or composite.
Does every number have 1 and itself as divisors?
Yes, for any whole number greater than 1. 1 divides every number, and every number divides itself. Those two divisors are the only ones a prime number has.
How many divisors does 1 have?
1 has only one divisor, itself, which is why 1 is classed as neither prime nor composite: the definition of a prime number requires exactly two distinct divisors.
Why does the calculator only check up to the square root of the number?
Divisors always come in pairs that multiply to the number: if i divides n, so does n ÷ i. Once i passes the square root, every remaining divisor has already been found as the pairing of a smaller one, so checking further would only repeat work.
To find the divisors two numbers share, see the GCD & LCM calculator. To break a number down into its prime building blocks instead of listing every divisor, use the prime check & factorisation calculator.