A common factor is a number that divides two or more numbers exactly without leaving any remainder. In other words, it is a factor shared by two or more numbers. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, and the factors of 16 are 1, 2, 4, 8, and 16. The common factors of 12 and 16 are 1, 2, and 4 because these numbers divide both 12 and 16 exactly
. To find common factors, you list all the factors of each number and then identify the numbers that appear in all lists. For instance, for the numbers 8, 12, 20, and 28, the common factors are 1, 2, and 4 because these divide all four numbers exactly
. The greatest common factor (GCF) is the largest number among the common factors. For example, the GCF of 12 and 16 is 4, since it is the biggest number that divides both exactly
. In summary:
- A factor is a number that divides another number exactly.
- A common factor divides two or more numbers exactly.
- The greatest common factor is the largest common factor shared by the numbers.
This concept is useful in simplifying fractions, factoring polynomials, and solving various mathematical problems involving divisibility
