Graduate Management Admission Test (GMAT) Practice Test

In the context of factors and multiples, which statement is true?

1. There are fewer factors than multiples

2. Factors can be infinite

3. Every integer has the same number of factors and multiples

4. There are finite factors and infinite multiples

The correct answer is: There are finite factors and infinite multiples

The statement that there are finite factors and infinite multiples is true because, for any given integer, the number of factors is limited by the integer's size and its prime factorization. Each factor corresponds to a whole number that divides the integer evenly, and since factors are based on the integer's specific composition, they can only be a finite set of numbers. In contrast, multiples of an integer can extend indefinitely. For any integer, you can multiply it by any positive whole number to create a new multiple. For example, the multiples of 3 include 3, 6, 9, 12, 15, and so on, theoretically going on forever. This fundamental difference between the two concepts highlights that while factors will always be a finite set tied to the integer, multiples can continue indefinitely for any positive integer.