Graduate Management Admission Test (GMAT) Practice Test

How are factors of a positive integer defined?

1. Numbers greater than the integer

2. Numbers that multiply to the integer

3. Numbers that divide evenly into the integer

4. Numbers that add up to the integer

The correct answer is: Numbers that divide evenly into the integer

Factors of a positive integer are defined as numbers that divide evenly into that integer without leaving a remainder. This means if you take a positive integer and a factor, when you divide the integer by that factor, the result is a whole number. For example, if we consider the integer 12, its factors are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder. In contrast, the other definitions presented in the choices do not accurately describe factors: - Numbers greater than the integer cannot be factors, as factors must be equal to or less than the integer itself. - Numbers that multiply to the integer is misleading because while factors do multiply together to form the integer, this description could apply to multiple pairs of factors rather than the factors themselves. - Numbers that add up to the integer describes a concept more related to sums rather than factors, which specifically pertains to division. Therefore, the correct understanding of factors aligns neatly with the definition given, confirming that they are indeed numbers that divide evenly into the integer.