Graduate Management Admission Test (GMAT) Practice Test

When considering multiples, how can they be described when compared to factors?

1. They are limited in number

2. They can be numerous and infinite

3. They are identical to factors

4. They always outnumber factors

The correct answer is: They can be numerous and infinite

When examining multiples in relation to factors, it is important to understand the fundamental definitions of each term. A multiple of a number is calculated by multiplying that number by integers. For instance, the multiples of 3 are 3, 6, 9, 12, and so forth, extending infinitely as you continue to multiply by larger integers. On the other hand, a factor of a number is a number that divides evenly into it. For the number 12, the factors are 1, 2, 3, 4, 6, and 12. Each of these factors can produce multiples, but the number of multiples is theoretically infinite because you can multiply by any positive integer. This is why multiples can be described as numerous and infinite. For any given number, there is no limit to how many multiples can be derived from it, whereas factors are finite and will always be fewer in number compared to the limitless multiples that can be generated from any integer. Thus, the correct understanding of multiples illustrates their expansive nature in contrast to the comparatively limited set of factors.