What is the greatest common factor of 49 and 48?

Answer 1

The GCF of 48 and 49 is 1. The GCF of any two consecutive integers is 1.

Definition: A factor is a divisor - a number that will evenly divide into another number. The common factors of two or more numbers are all the factors that the numbers have in common. The greatest common factor of two or more numbers is the largest factor that the numbers have in common.

Method:

One way to determine the common factors and greatest common factor is to find all the factors of the numbers and compare them.

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The factors of 49 are 1, 7, and 49.

The only common factor is 1. Therefore, the greatest common factor is 1, which means the numbers are relatively prime.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. To then obtain the common factors, list all the factors of the greatest common factor.

The prime factors of 48 are 2, 2, 2, 2, and 3.

The prime factors of 49 are 7 and 7.

There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor (and only common factor) is 1.