Graduate Management Admission Test (GMAT) Practice Test

Which of the following defines a prime number?

1. A positive integer greater than 1

2. An integer divisible by multiple factors

3. A positive integer divisible only by 1 and itself

4. A whole number with no factors

The correct answer is: A positive integer divisible only by 1 and itself

A prime number is defined specifically as a positive integer greater than 1 that has no positive divisors other than 1 and itself. This means that it cannot be formed by multiplying two smaller positive integers. For example, the number 5 is prime because the only positive integers that can divide it without leaving a remainder are 1 and 5. The definition in the correct choice captures both essential characteristics of a prime number: its positivity and the exclusivity of its factors. Notably, prime numbers begin at 2, the smallest and only even prime, and include other numbers such as 3, 5, 7, 11, etc. The other options either misdefine or do not adequately describe what a prime number is: - A positive integer greater than 1, while true for primes, is incomplete because it does not specify that it must be divisible only by 1 and itself. - An integer divisible by multiple factors describes composite numbers, which have more than two divisors. - A whole number with no factors is misleading, as this could imply that the number is 0 or a negative integer, which do not fit the definition of prime numbers, where specifically only positive integers greater than 1 are considered.