What is the relationship between common factors and greatest common factors?

Answer 1

Common factors are factors that are shared by a given set of numbers, usually positive integers.

Greatest common factors (sometimes abbreviated to GCFs) are the factors in these given sets that have the greatest value out of all common factors.

Example:

Factors of 9: 1, 3, 9

Factors of 15: 1, 3, 5, 15

The common factors of 9 and 15: 1, 3

The GCF: 3

Answer 2

Factors are numbers that multiply to become a product.

Common factors are factors that are part of more than one number's list of factors.

The greatest common factor is the largest of the common factors.

Example: 30, 42

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The common factors are 1, 2, 3, 6

The Greatest Common Factor (GCF) is 6

Answer 3

A factor of a number is a number that number can be divided by. For instance, 20 has the factors 1, 2, 4, 5, 10 and 20. 28 has the factors 1, 2, 4, 7, 14 and 28. Common factors are factors which appear in both lists. In this instance, 1, 2 and 4 are common factors of 20 and 28. The greatest common factor is the biggest number out of the common factors. In this case, 4 is the greatest common factor.

Answer 4

The greatest common factor, or GCF, is the largest number in the set of common factors.

Answer 5

In any set of common factors, the largest number is the GCF.

Answer 6

All numbers have factors. Some numbers have some of the same factors as other numbers. These are known as common factors. The largest of these is known as the greatest common factor, or GCF.