What is the greatest common factor of 12 20 and 26?

Answer 1

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

The factors of 12 are 1, 2, 3, 4, 6, and 12.

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

The factors of 26 are 1, 2, 13, and 26.

The common factors are 1 and 2. Therefore, the greatest common factor is 2.

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

The prime factors of 12 are 2, 2, and 3.

The prime factors of 20 are 2, 2, and 5.

The prime factors of 26 are 2 and 13.

The prime factors in common are a single 2, so the greatest common factor is 2.

Another way to approach this is to look at the differences between the numbers. The difference between 12 and 20 is 8. The difference between 20 and 26 is 6. The greatest common factor cannot be greater than the smallest difference between the numbers, and must be a factor of the differences between the numbers. So, the greatest common factor of 6 and 8 will also be the greatest common factor of 12, 20, and 26. Next, you can compare the difference of the differences: the difference between 6 and 8 is 2, which divides both 6 and 8, so the greatest common factor of 6 and 8 is 2. Thus, the greatest common factor of 12, 20, and 26 is 2.2
12

6,2

3,2,2

20

10,2

5,2,2

26

2,13

The only common factor is 2, the GCF.

Answer 2

GCF of 12 and 20 and 26 is 2.