Common Factor Calculator
List all factors shared by a set of numbers, not just the greatest one.
About Common Factor Calculator
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)
Worked example
With the default values below, Common Factor Calculator returns Greatest Common Factor of 12. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numbers (comma or space separated)
- 24, 36, 60
Results
- Greatest Common Factor
- 12
- Number of Common Factors
- 6
- All Common Factors
- 1, 2, 3, 4, 6, 12
Step by step
- 1Inputs= 24, 36, 60
- 2GCF (the key insight)= 12Every divisor of the GCF is a common factor of all numbers.
- 3Common factors (6)= 1, 2, 3, 4, 6, 12
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.