Greatest Common Factor Calculator

Your details

Two or more whole numbers separated by commas or spaces. Signs are ignored; zeros are skipped.
All three methods give the same answer. Euclidean is best for large numbers; prime factorization shows the structure; listing factors is easiest to follow by hand for small numbers.
The least common multiple (LCM) is related to the GCF by: GCF x LCM = product of the numbers (for pairs).
Greatest common factor (GCF)Common factor found
12
Numbers used3
Total common factors6
All common factors1, 2, 3, 4, 6, 12
Least common multiple (LCM)360
RelationshipShared factor: 12
GCF12
Common factor count6

The greatest common factor is 12.

  • Every number you entered is exactly divisible by 12, and no larger integer is.
  • There are 6 common factors in total; the GCF is the largest of these.
  • To reduce a fraction whose numerator and denominator are two of these numbers, divide both by 12 to reach lowest terms.
  • The Euclidean algorithm finds the GCF without full factorisation: gcf(a, b) = gcf(b, a mod b), repeated until the remainder is zero.

Next stepThe least common multiple of your numbers is 360. This is the smallest number all of them divide into evenly.

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