Common Factor Calculator
Enter two or more positive whole numbers, separated by commas or spaces, and press Find Common Factors. The calculator returns the greatest common factor and lists every common factor, because each one divides the GCF. The GCF keeps all its digits at any size. The list stops at a GCF of 1,000,000,000,000, and above that the page says so.
How to use the Common Factor Calculator
- Enter your numbers in the Common Factor Calculator above.
- Press the Find GCF button to see the result.
- To try other numbers, change any value and press the button again.
The common factors approach
Common factors of (a, b, ...) = factors of GCD(a, b, ...)
The factors common to multiple numbers are exactly the factors of their greatest common divisor. The calculator finds the GCD, then tests each whole number up to its square root to list all its factors.
Worked example
Enter 24, 36 and the calculator returns 12 as the GCF and lists the factors of 12, which are 1, 2, 3, 4, 6 and 12. Enter 18, 24, 60 and it returns 6, with the common factors 1, 2, 3 and 6.
Frequently asked questions
Does it list every common factor?
Yes, up to a GCF of 1,000,000,000,000, the same limit as the factor calculator. Above that the calculator still returns the exact GCF, but listing its factors would take too long, so it says so instead.
Can two numbers share no common factor?
Two numbers always share 1 as a common factor. If 1 is the only common factor, the numbers are coprime (or relatively prime).
How does this help with fractions?
When simplifying a fraction, you divide top and bottom by any common factor. The fraction is fully simplified when the only common factor is 1.