What is the greatest common factor of 9 27 and 60?

Answer 1

One way to find the greatest common factor is to look at the factors of the smallest number and see whether any of them evenly divide the other numbers. This works well when one number is small or has very few factors. The factors of 9 are 1, 3, and 9. Although 9 evenly divides 27, it does not evenly divide 60. So, check the next largest factor of 9, which is 3. Both 27 and 60 are divisible by 3, so 3 is the greatest common factor.

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

The factors of 9 are 1, 3, and 9.

The factors of 27 are 1, 3, 9, and 27.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

The common factors are 1 and 3. Therefore, the greatest common factor is 3.

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

The prime factors of 9 are 3 and 3.

The prime factors of 27 are 3, 3, and 3.

The prime factors of 60 are 2, 2, 3, and 5.

The prime factors in common are a single 3, so the greatest common factor is 3.