Let p be the product of the positive integers between 1 and 7, inclusive. How many distinct prime factors does p have? A. 1 B. 2 C. 3 D. 4 E. 5

(D) is the correct answer. The first step is to determine which product we are actually concerned with. The positive integers between 1 and 7 inclusive are 7, 6, 5, 4, 3, 2, 1. We don't have to multiply them out just yet. We can break them up in to their prime components: 7 × 6 × 5 × 4 × 3 × 2 × 1 = 7 × (2 × 3) × 5 × (2 × 2) × 3 × 2 × 1. Notice that the only prime factors that appear are 2, 3, 5 and 7 (remember that 1 is not a prime number).

------------- Why do we not count 1 as a prime number?

When the question stated 'between 1 and 7', I assumed that meant the numbers between 1 and 7, not inclusive. When the question is stated like so, should I always assume that this would include 1 and 7 on the GMATs?

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