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## Official Guide Explanation:

Problem Solving #D18

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: D18**

Page: 22

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Properties of Integers > Factors and Multiples

**Explanation:** n is equal to (1)(2)(3)(4)(5)(6)(7)(8). Don't multiply all those numbers! The largest possible prime factor of the product must be no larger than 8. There's no way for, say, 11 to be a prime factor unless 11 (or a multiple of 11) is one of the numbers multiplied to get the product.

Thus, the only possible prime factors are 2, 3, 5, and 7, the primes less than 8. Since all four of those numbers are present in the list of numbers to be multiplied, all are factors of the product. Thus, there are 4 different prime factors of n, choice (A).

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