This common factor calculator lists every positive factor shared by two integers. For the defaults a = 36 and b = 60 the common factors are 1, 2, 3, 4, 6, and 12. The greatest value in that list is 12, but the page is not limited to the GCF alone.
When you only need the greatest common factor, use the GCF calculator. To factor a single integer, open the factor calculator.
How the formula works
Compute g = gcd(a, b). Every positive divisor of g is a common factor of a and b. Listing those divisors produces the full common factor set in ascending order.
Worked example
gcd(36, 60) = 12. Positive divisors of 12 are 1, 2, 3, 4, 6, and 12. Each divides both 36 and 60. No larger shared positive factor exists.
| Input | Value |
|---|---|
| Number A | 36 |
| Number B | 60 |
| GCF | 12 |
| Common factors | 1, 2, 3, 4, 6, 12 |
How to use the fields
- Number A is the first positive integer.
- Number B is the second positive integer.
Common factors versus GCF
Searchers often type “common factor” when they want the whole list, and “GCF” when they want a single champion value. Keeping both pages distinct prevents confusion. Here the teaching goal is the set; the GCF is simply the last entry when the list is sorted.
Simplifying fractions uses the GCF. Listing factor pairs for word problems may need several common factors, not only 12.
Common mistakes
- Reporting only 12 and calling the task finished when the prompt asked for all common factors
- Including 18, which divides 36 but not 60
- Forgetting 1, which is always a common factor for positive integers
- Listing factors of only one number
Hand check without gcd first
List factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. List factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The intersection is 1, 2, 3, 4, 6, 12. Matching the gcd method builds confidence.
For larger inputs, the gcd route is faster than building two full factor lists.
Classroom uses
Ask whether 9 is common: it divides 36 but not 60, so it must not appear. Ask whether 4 is common: both divide evenly, so it must appear. Those yes/no checks beat memorizing the finished list.
Connect to fraction reduction: 36/60 divides by any common factor; dividing by 12 yields the fully reduced 3/5.
Coprime pairs
If gcd is 1, the common factor list is only 1. That outcome is useful for proving two integers share no larger positive divisor. Try nearby numbers until students see both rich lists and singleton lists.
Order and duplicates
The tool lists each positive common factor once in increasing order. You do not need to dedupe by hand. When writing answers, keep commas consistent with the display.
Percent style reporting of “how many common factors” can use the percentage calculator only if a worksheet asks for a share of a larger set; the factor list itself stays integer work.
Why the full list still matters
Teachers may ask for any common factor that simplifies a ratio, not only the greatest. With 36 and 60, dividing by 6 yields 6/10, which still needs another step, while dividing by 12 finishes in one step. Showing 1, 2, 3, 4, 6, and 12 makes that pedagogy visible.
Contest problems sometimes forbid using the GCF directly and instead require proving a smaller factor works. Having the complete list ready saves time.
Keep the GCF calculator bookmarked for the single number case, and keep this page for the set. That split matches how search queries differ in practice.
End with a fresh pair such as 48 and 180, predict the GCF, then expand to the full common factor list before confirming with the tool. Prediction first keeps the calculator honest as a check.
Remember that the default teaching pair still returns 1, 2, 3, 4, 6, and 12, with 12 as the greatest entry rather than the only answer.
That distinction from a GCF only page is the main reason this calculator exists.
Limitations
Positive integers only in this educational path. No prime factorization display beyond what you infer from the list, and no LCM on this page.