What is the greatest common factor (GCF) of 8 and 12?

What is the greatest common factor (GCF) of 8 and 12?

• A. 2
• B. 4
• C. 6
• D. 8

Answer: (B)

To find the greatest common factor (GCF) of 8 and 12, we begin by identifying the factors of each number. The factors of 8 are: 1, 2, 4, 8. The factors of 12 are: 1, 2, 3, 4, 6, 12. Next, we look for the common factors between the two sets. The common factors of 8 and 12 are: 1, 2, and 4. Among these common factors, the greatest one is 4. Therefore, the greatest common factor of 8 and 12 is indeed 4. This means that 4 is the largest number that divides both 8 and 12 without leaving a remainder. Understanding this process is crucial because it shows how to systematically determine the GCF, which is useful for simplifying fractions, finding common denominators, and solving problems involving ratios.

To find the greatest common factor (GCF) of 8 and 12, we begin by identifying the factors of each number.

The factors of 8 are:

1, 2, 4, 8.

The factors of 12 are:

1, 2, 3, 4, 6, 12.

Next, we look for the common factors between the two sets. The common factors of 8 and 12 are:

1, 2, and 4.

Among these common factors, the greatest one is 4. Therefore, the greatest common factor of 8 and 12 is indeed 4. This means that 4 is the largest number that divides both 8 and 12 without leaving a remainder.

Understanding this process is crucial because it shows how to systematically determine the GCF, which is useful for simplifying fractions, finding common denominators, and solving problems involving ratios.