About the Common Factor Calculator
A common factor calculator lists every number that divides two integers evenly, not just the largest. Seeing the full set is useful when you need a convenient divisor rather than the greatest one — splitting into groups of a workable size, or choosing a scale factor.
The formula
Common factors of a and b = all divisors of GCD(a, b)Every common factor of two numbers divides their greatest common divisor, so the complete list of common factors is exactly the list of divisors of the GCD.
How to use this calculator
- 1Enter your Number A. The field starts at
36, which you can overwrite. - 2Enter your Number B. The field starts at
48, which you can overwrite. - 3Read 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 A | 36 |
| Number B | 48 |
Result
GCD: 12
LCM: 144
Common Factors: 1, 2, 3, 4, 6, 12
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
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
That relationship is the neat result here: you do not need to factor both numbers and intersect the lists. Find the GCD once, then list its divisors. For 36 and 48 the GCD is 12, whose divisors are 1, 2, 3, 4, 6, and 12 — and those are precisely the common factors of the original pair.
Which one you want depends on the task. Reducing a fraction to lowest terms needs the greatest. Dividing 36 chairs and 48 tables into identical sets might be better served by 6 sets than 12, if 12 sets would be too small to be useful. Having the full list lets you choose on practical grounds rather than mathematical ones.
Things worth knowing
- 1 is a common factor of every pair of integers, so the list is never empty.
- If the only common factor is 1, the numbers are coprime.
- The number of common factors equals the number of divisors of the GCD.
- Any common factor divides the sum and difference of the two numbers as well.
- For three or more numbers, take the GCD of all of them and list its divisors.
Frequently asked questions
What is a common factor?+
A number that divides two or more integers with no remainder. The common factors of 36 and 48 are 1, 2, 3, 4, 6, and 12, each dividing both numbers exactly.
How do I find all common factors quickly?+
Compute the greatest common divisor, then list its divisors. Every common factor divides the GCD, so this gives the complete set without factoring both numbers separately.
Do all pairs of numbers have a common factor?+
Yes — 1 always divides both. When 1 is the only one, the numbers are coprime, which is the case for any two consecutive integers.
When would I want a common factor other than the greatest?+
When the greatest produces an impractical result. Splitting quantities into groups, choosing a drawing scale, or picking a step size often calls for a convenient divisor rather than the largest possible one.