About the Factor Calculator
A factor calculator lists every whole number that divides evenly into your number, along with its prime factors. Factoring underlies simplifying fractions, finding common denominators, and much of number theory — and it is the problem whose difficulty at scale protects modern encryption.
The formula
f is a factor of n if n mod f = 0A factor divides n with no remainder. A prime factor is a factor that is itself prime — divisible only by 1 and itself.
How to use this calculator
- 1Enter your Number. The field starts at
60, which you can overwrite. - 2Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Number | 60 |
Result
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Number of Factors: 12
Prime Factorization: 2 × 2 × 3 × 5
Perfect Square: No
Prime: No
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Factors come in pairs. If 4 divides 60, then so does 15, because 4 × 15 = 60. This is why you only need to test divisors up to the square root of a number to find all its factors: each divisor below the square root has a partner above it. It is also why factoring is fast for small numbers.
Every integer greater than 1 has a unique prime factorisation — the fundamental theorem of arithmetic. 60 is 2² × 3 × 5 and can be written that way in exactly one manner. That uniqueness is what makes prime factorisation the basis for computing greatest common divisors and least common multiples reliably.
Things worth knowing
- Perfect squares have an odd number of factors, because one divisor pairs with itself.
- A prime number has exactly two factors: 1 and itself. That is the definition.
- Quick divisibility checks: by 2 if the last digit is even, by 3 if the digit sum divides by 3, by 5 if it ends in 0 or 5, by 9 if the digit sum divides by 9.
- The number 1 is neither prime nor composite — a convention that keeps prime factorisation unique.
- RSA encryption rests on the difficulty of factoring the product of two very large primes.
Frequently asked questions
What is the difference between a factor and a multiple?+
A factor divides into a number; a multiple is produced by multiplying it. 4 is a factor of 12, and 12 is a multiple of 4. Factors are never larger than the number, multiples never smaller.
How do I find all the factors of a number?+
Test every integer from 1 up to the square root. Each divisor you find gives a paired factor when you divide the number by it, so the pairs together form the complete list.
Is 1 a prime number?+
No. Primes are defined as having exactly two distinct factors, and 1 has only one. Excluding it is what makes prime factorisation unique for every other integer.
What are prime factors used for?+
Simplifying fractions, computing greatest common divisors and least common multiples, and solving number theory problems. In cryptography, the difficulty of finding the prime factors of very large numbers is what secures RSA.