How to find factors
A factor divides a number evenly. To find them all, test each value from 1 up to the square root of the number — whenever one divides cleanly, it and its partner are both factors:
If d divides n, then d and n ÷ d are both factors
For 60, that gives 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 — twelve factors in all, summing to 168.
Prime factorization
Breaking a number into its prime building blocks gives 60 = 2² × 3 × 5. From that you can read off the factor count by adding one to each exponent and multiplying: (2+1)(1+1)(1+1) = 12. For greatest-common and least-common work, see the GCF and LCM calculators.
Frequently asked questions
What is a factor of a number?
A factor (or divisor) is a whole number that divides another number evenly, with no remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12, because each divides 12 exactly. Every number has at least two factors: 1 and itself.
What is prime factorization?
Prime factorization breaks a number down into the prime numbers that multiply to make it. For 60, that is 2 × 2 × 3 × 5, written 2² × 3 × 5. Every whole number greater than 1 has exactly one prime factorization.
How do you find all the factors of a number?
Check each number from 1 up to the square root; whenever one divides evenly, both it and its pair (the number divided by it) are factors. This is far faster than testing every number up to the original, and it is how the calculator works.
What is a prime number?
A prime number has exactly two factors: 1 and itself. Examples are 2, 3, 5, 7, and 11. If a number has any factors besides 1 and itself, it is called composite. The calculator tells you which one your number is.
How many factors does a number have?
Take the exponents in the prime factorization, add one to each, and multiply them. For 60 = 2² × 3¹ × 5¹, that is (2+1)(1+1)(1+1) = 12 factors. The calculator counts them directly and shows the total.
Disclaimer: For performance, the input is capped at one trillion. Results are provided for educational purposes.