Common Factor Calculator
List all common factors shared by a set of numbers — every shared divisor, not just the greatest.
Inputs
Greatest Common Factor
12
Number of Common Factors
6
All Common Factors
1, 2, 3, 4, 6, 12
Step by step
Inputs
= 24, 36, 60
GCF (the key insight)
GCF of 24, 36, 60 = 12
= 12
Every divisor of the GCF is a common factor of all numbers.
Common factors (6)
= 1, 2, 3, 4, 6, 12
How it works
A common factor of a set of integers is a positive number that divides each of them exactly. The set of all common factors is exactly the set of all divisors of the GCF — this follows from the definition of GCF. For example, the common factors of 24, 36 and 60 are the factors of GCF(24, 36, 60) = 12: that's 1, 2, 3, 4, 6, 12.
Formula
Key relationship
The set of common divisors of a and b equals the set of divisors of gcd(a, b)
Frequently Asked Questions
What is the difference between common factors and the GCF?
Common factors are all the divisors shared by the numbers. The GCF (Greatest Common Factor) is just the largest of those shared divisors. For 24 and 36, common factors are 1, 2, 3, 4, 6, 12; the GCF is 12.
Do 1 and the GCF always appear in the common factors?
Yes. 1 always divides every integer. The GCF always divides every number in the list by definition. Every divisor of the GCF (including 1 and the GCF itself) is a common factor.
How many common factors can two numbers have?
As many as the GCF has divisors. For large GCFs this can be substantial: gcd(360, 420) = 60, which has 12 divisors — so there are 12 common factors.