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## Official Guide Explanation:Problem Solving #107

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.

Question: 107
Page: 167
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: The question is essentially asking us to find the prime factorization of 8!. If we break down each of the first eight integers to their prime factors, we get the following:

8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

= 23 * 7 * 2(3) * 5 * 22 * 3 * 2

Now combine each of the prime factors:

= 27 * 32 * 51 * 71

The four exponents (i, k, m, and p in the problem) are 7, 2, 1, and 1, for a sum of 11, choice (D).

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