What is the GCF of two numbers?

What is the GCF of two numbers?

• A. The smallest number that divides both numbers
• B. The greatest factor that divides both numbers
• C. The sum of the two numbers
• D. The product of the two numbers

Answer: (B)

The greatest common factor (GCF) of two numbers is defined as the largest positive integer that divides both numbers without leaving a remainder. Therefore, when considering the options, the choice that accurately describes this concept is one that refers to the greatest factor that divides both numbers. This means it focuses on the commonality shared between the factors of the two numbers and identifies the largest of those shared factors. By this definition, the GCF is not concerned with the smallest number that divides both (which can lead to confusion, as smaller factors might also divide the numbers), nor does it pertain to the sum or product of the two numbers, which are entirely different mathematical concepts unrelated to common factors. Thus, the correct characterization emphasizes the largest common divisor rather than a simplistic view of divisibility or summation.

The greatest common factor (GCF) of two numbers is defined as the largest positive integer that divides both numbers without leaving a remainder. Therefore, when considering the options, the choice that accurately describes this concept is one that refers to the greatest factor that divides both numbers. This means it focuses on the commonality shared between the factors of the two numbers and identifies the largest of those shared factors.

By this definition, the GCF is not concerned with the smallest number that divides both (which can lead to confusion, as smaller factors might also divide the numbers), nor does it pertain to the sum or product of the two numbers, which are entirely different mathematical concepts unrelated to common factors. Thus, the correct characterization emphasizes the largest common divisor rather than a simplistic view of divisibility or summation.