What is the greatest common factor (GCF) of 12 and 15?

What is the greatest common factor (GCF) of 12 and 15?

• A. 1
• B. 3
• C. 5
• D. 6

Answer: (B)

To determine the greatest common factor (GCF) of 12 and 15, we begin by identifying the factors of each number. The factors of 12 are: 1, 2, 3, 4, 6, 12 The factors of 15 are: 1, 3, 5, 15 Next, we find the common factors from these two lists, which are the numbers that appear in both sets of factors. The common factors of 12 and 15 are: 1 and 3. Among these common factors, the greatest one is 3. Hence, the GCF of 12 and 15 is 3, making this the correct answer. This method illustrates how to systematically identify factors and determine the greatest common factor, which is a fundamental skill in number theory and is useful for simplifying fractions, solving problems involving divisibility, and working with ratios.

To determine the greatest common factor (GCF) of 12 and 15, we begin by identifying the factors of each number.

The factors of 12 are:

1, 2, 3, 4, 6, 12

The factors of 15 are:

1, 3, 5, 15

Next, we find the common factors from these two lists, which are the numbers that appear in both sets of factors. The common factors of 12 and 15 are:

1 and 3.

Among these common factors, the greatest one is 3. Hence, the GCF of 12 and 15 is 3, making this the correct answer.

This method illustrates how to systematically identify factors and determine the greatest common factor, which is a fundamental skill in number theory and is useful for simplifying fractions, solving problems involving divisibility, and working with ratios.