What is the greatest common factor of 180 and 210?

What is the greatest common factor of 180 and 210?
One way to approach this is to look at the difference between 180 and 210, which is 30. The greatest common factor of two numbers cannot be larger than the difference between the two numbers. Since both 180 and 210 are divisible by 30, the greatest common factor is 30.

Another way to determine the greatest common factor is to find all the factors of the numbers and compare them.
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 factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
The common factors are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the greatest common factor is 30.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.
The prime factors of 180 are 2, 2, 3, 3, and 5.
The prime factors of 210 are 2, 3, 5, and 7.
The prime factors in common are 2, 3, and 5, so the greatest common factor is 2 x 3 x 5 = 30.