The formula
How it works
List every whole number that divides evenly into a given number — its factors. Enter a number and see all its factors, how many there are, and whether it is prime.
FAQ
What is the difference between a factor and a multiple?
A factor divides into a number exactly (6 is a factor of 12), while a multiple is what you get by multiplying it (24 is a multiple of 12). Factors are always less than or equal to the number; multiples are greater than or equal to it.
How do I know if a number is prime?
A prime number has exactly two factors: 1 and itself. If the calculator lists only two factors, the number is prime; more than two means it is composite.
How are factors related to the greatest common factor (GCF)?
The GCF of two numbers is the largest factor they share. List the factors of each number with this calculator, then pick the biggest value that appears in both lists.
How are factors related to the least common multiple (LCM)?
Factors and multiples work in opposite directions, but they connect through the identity GCF × LCM = the product of the two numbers. Once you know a number’s factors, you can use this relationship to find its LCM with another number.
Are 1 and the number itself always factors?
Yes — every whole number greater than 0 is divisible by 1 and by itself, so both always appear in the factor list. That is exactly why a prime number, which has no other factors, ends up with only two.
Why do some numbers have an odd number of factors?
Factors normally come in pairs (like 4 and 15 for 60), but a perfect square has one factor that pairs with itself — its square root — so the total count comes out odd. 36, for example, has 9 factors because 6 × 6 = 36.
Can I factor a negative number?
This calculator works with the absolute value of the number you enter, since factors are usually discussed for positive whole numbers. The same factor list applies to a negative number, just paired with both positive and negative divisors in full number theory.
About the factor calculator
This calculator finds all the factors of a whole number — every number that divides into it without leaving a remainder. Factors are a building block of arithmetic: they are the key to simplifying fractions, finding common denominators, and understanding whether a number is prime. Rather than testing divisors one by one, this tool lists them all at once and tells you how many there are.
How to use it
Type a whole number and the calculator lists all of its factors in order, from 1 up to the number itself. For example, 60 has the factors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 — twelve in total. It also flags whether the number is prime (exactly two factors) and shows the sum of its factors, which comes up in number-theory puzzles.
The formula
A number is a factor of when it divides in exactly, which is written and means — the remainder is zero. To find them all efficiently, you only need to test divisors up to : each small factor pairs with a larger one , so factors come in pairs around the square root. The calculator collects both members of each pair.
Where it is used
Factoring is used constantly in maths. Simplifying a fraction means dividing by a common factor, adding fractions needs common denominators built from factors, and greatest common factor and least common multiple both start here. It also matters in scheduling and grouping problems, and the difficulty of factoring very large numbers is what keeps a lot of modern encryption secure.