Which statement best defines the common factor?

Which statement best defines the common factor?

• A. A factor of all numbers combined
• B. A factor of two or more given numbers
• C. The largest multiple of two numbers
• D. The sum of the numbers' factors

Answer: (B)

A common factor is a number that divides each number in the given set evenly. For two or more numbers, a common factor is a divisor that appears in the factor lists of all of them. That’s why the best description is “a factor of two or more given numbers”—it means the number divides every one of the numbers under consideration. For example, with 8 and 12, the common factors are 1, 2, and 4, since each divides both numbers. The other statements stray from this idea: a factor of all numbers combined could mean something like a divisor of a sum or product, which isn’t the definition; a largest multiple isn’t about divisors; and the sum of the numbers’ factors isn’t about divisibility at all.

A common factor is a number that divides each number in the given set evenly. For two or more numbers, a common factor is a divisor that appears in the factor lists of all of them. That’s why the best description is “a factor of two or more given numbers”—it means the number divides every one of the numbers under consideration. For example, with 8 and 12, the common factors are 1, 2, and 4, since each divides both numbers. The other statements stray from this idea: a factor of all numbers combined could mean something like a divisor of a sum or product, which isn’t the definition; a largest multiple isn’t about divisors; and the sum of the numbers’ factors isn’t about divisibility at all.