Which statement correctly defines the greatest common factor (GCF)?

Which statement correctly defines the greatest common factor (GCF)?

• A. The smallest factor that two numbers have in common
• B. The largest factor that two or more numbers have in common
• C. A number that is a factor of only one of the given numbers
• D. The same as the least common multiple

Answer: (B)

The greatest common factor is the largest positive integer that divides each of the given numbers exactly. So saying it is the largest factor that two or more numbers have in common matches that idea. The other descriptions miss essential points: the smallest common factor isn’t the GCF; a number that only divides one of the numbers isn’t shared by all, so it can’t be the GCF; and the GCF is not the same as the least common multiple, which is the smallest number divisible by all the given numbers.

The greatest common factor is the largest positive integer that divides each of the given numbers exactly. So saying it is the largest factor that two or more numbers have in common matches that idea. The other descriptions miss essential points: the smallest common factor isn’t the GCF; a number that only divides one of the numbers isn’t shared by all, so it can’t be the GCF; and the GCF is not the same as the least common multiple, which is the smallest number divisible by all the given numbers.