What is the greatest common factor of 144 and 180?

Answer 1

One way to approach this is to look at the difference between 144 and 180, which is 36. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. Since both 144 and 180 are divisible by 36, the greatest common factor is 36.

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

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

The common factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Therefore, the greatest common factor is 36.

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

The prime factors of 144 are 2, 2, 2, 2, 3, and 3.

The prime factors of 180 are 2, 2, 3, 3, and 5.

The prime factors in common are 2, 2, 3, and 3, so the greatest common factor is 2 x 2 x 3 x 3 = 36.