Find all common factors (divisors) shared between two or more numbers, identify the greatest common factor, and view Venn intersection tables.
Common factors are integers that divide evenly into two or more given numbers without leaving a remainder. In mathematical set notation, the common factors of a set of numbers represent the set intersection of their individual factor lists: Factors(A) ∩ Factors(B). The largest member of this intersection is the Greatest Common Factor (GCF).
The number 1 is a divisor of all positive integers, so 1 is guaranteed to be a common factor of every group of integers.
When two or more integers share no common factors other than 1, they are called coprime or relatively prime (e.g. 14 and 15).
A common factor cannot exceed the smallest number in the input list, nor can it exceed the difference between consecutive numbers.
Dividing all numbers by any valid common factor yields smaller integers while preserving their relative ratios.
List the divisors of 24 and 36, find their common factors, and identify the GCF.
Two distinct prime numbers p and q share only the number 1 as a common factor, meaning any two distinct primes are always mutually coprime.
Common factors are used when tiling floors evenly without cutting tiles, dividing groups of students into equal teams, packaging goods into uniform boxes, and arranging items in grid formations.
Yes, in algebra, common factors can include negative integers (e.g. ±1, ±2, ±3, ±6), although positive common factors are typically reported by default.
The number of common factors of A and B is exactly equal to the total number of divisors of their Greatest Common Factor, d(GCF(A, B)).
Understanding your calculation
Common factors are positive integers that divide every entered integer exactly. The greatest common factor is the largest member of that list.
The common positive factors of 12 and 18 are 1, 2, 3 and 6.
Common factors are different from common multiples. Integer size and zero-input conventions can affect supported results.