What is the greatest common factor of 80 and 72?
One way to approach this is to look at the difference between 72
and 80, which is 8. The greatest common factor of two numbers
cannot be larger than the difference between the two numbers. Since
both 72 and 80 are divisible by 8, the greatest common factor is
8.
Another way to determine the greatest common factor is to find
all the factors of the numbers and compare them.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and
72.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The common factors are 1, 2, 4, and 8. Therefore, the greatest
common factor is 8.
The greatest common factor can also be calculated by identifying
the common prime factors and multiplying them together.
The prime factors of 72 are 2, 2, 2, 3, and 3.
The prime factors of 80 are 2, 2, 2, 2, and 5.
The prime factors in common are 2, 2, and 2, so the greatest
common factor is 2 x 2 x 2 = 8.