What is the greatest common factor of 40 60 and 120?

Answer 1

One way to approach this is to look at the differences between the numbers. The difference between 40 and 60 is 20. The difference between 60 and 120 is 60. The greatest common factor of two or more numbers cannot be larger than the smallest difference between two of the numbers and must be a factor of the difference. The smallest difference is 20. All three numbers are divisible by 20, so the greatest common factor is 20.

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

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

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

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

The common factors are 1, 2, 4, 5, 10, and 20. Therefore, the greatest common factor is 20.

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

The prime factors of 40 are 2, 2, 2, and 5.

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

The prime factors of 120 are 2, 2, 2, 3, and 5.

The prime factors in common are 2, 2, and 5, so the greatest common factor is 2 x 2 x 5 = 20.

And one more way to find the greatest common factor is to make a reasonable guess and refine it. Since all the numbers end with 0, they are all divisible by 10, so divide by 10 and then examine the results.

40 ÷ 10 = 4

60 ÷ 10 = 6

120 ÷ 10 = 12

All of these results are even, so divide the results by 2.

4 ÷ 2 = 2

6 ÷ 2 = 3

12 ÷ 2 = 6

There are no common factors of 2, 3, and 6, so the greatest common factor is the product of the two numbers by which you divided, which is 10 x 2 = 20.