Common Factor Calculator
A shortcut for the shared list
Comparing two full factor lists works, but there is a faster route: every number common to both must divide their greatest common factor. For 12 and 18 the GCF is 6, whose divisors 1, 2, 3, and 6 are exactly the common factors — no longer lists required. That same GCF is what simplifies the ratio 12 : 18 down to 2 : 3 and reduces the fraction 12/18 to 2/3. When the GCF comes out as 1, the two numbers are called coprime or relatively prime, meaning their only shared factor is 1 even if each is individually composite.
Frequently Asked Questions
Can two numbers have a lot of common factors?
Yes — the count equals the number of divisors of the GCF. Highly divisible pairs like 360 and 720 share 24 common factors, while consecutive integers always share exactly one, since gcd(n, n+1) = 1.
Does this work for negative numbers?
Factors are defined by divisibility, so signs do not change the answer. Enter positive values here; if you have negatives, drop the minus signs and factor the absolute values.