What is the greatest common divisor of 12 and 30?

To find the greatest common divisor (GCD) of two numbers, we need to identify the largest number that divides both without leaving a remainder.

First, we can list the factors of each number:

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

• The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.

Next, we compare the factors of both numbers to find the common factors:

The common factors of 12 and 30 are: 1, 2, 3, and 6.

Among these common factors, the largest one is 6. Thus, the greatest common divisor of 12 and 30 is indeed 6. This value is significant because it represents the highest number that can exactly divide both original numbers, indicating a shared divisibility that is useful in many mathematical concepts, such as simplifying fractions.

The other values listed do not represent the largest common factor of the two numbers; therefore, they do not fulfill the criteria of being the greatest common divisor.