Definition
Common factor
A common factor is a positive whole number that divides each of two or more numbers exactly.
What it means
List the factors of each number, then look for numbers that appear in every list. Those shared divisors are the common factors. The word common means “shared”; it does not mean the factor appears many times in one list.
Remember it
Common factors are shared keys: each one unlocks every number with exact division.
Example
The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Their common factors are 1, 2, 3, and 6.
Watch for
4 is a factor of 24 but not of 18, so 4 is not a common factor of 18 and 24.
Common mix-up
A common factor divides the given numbers; a common multiple is divided by the given numbers.
Exact meaning
A common factor of two or more positive integers is a positive integer that divides every one of them with no remainder.