Official Guide Explanation:
Problem Solving #107

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Solution and Metadata

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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