What is the greatest common factor of 48 80 and 128?

Answer 1

Answer: 16

One way to determine the 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 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.

The common factors are 1, 2, 4, 8, and 16. Therefore, the greatest common factor is 16.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

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

The prime factors of 80 are 2, 2, 2, 2, and 5.

The prime factors of 128 are 2, 2, 2, 2, 2, 2, and 2.

The prime factors in common are 2, 2, 2, and 2, so the greatest common factor is 2 x 2 x 2 x 2 = 16.

Another way to approach this is to look at the differences between the numbers. The greatest common factor of two or more numbers cannot be larger than the smallest difference between the numbers. The difference between 48 and 80 is 32. The difference between 80 and 128 is 48. Also, the greatest common factor must be a factor of the differences between the numbers. If we find the greatest common factor of 32 and 48, we will have the greatest common factor of 48, 80, and 128. The difference between 32 and 48 is 16, so the greatest possible common factor between 32 and 48 is 16. Since 16 is a factor of both 32 and 48, it is their greatest common factor, and thus the greatest common factor of 48, 80, and 128.