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What is the largest integer \(n\) such that \(7^n\) divides 1000! and the answer isn't 163

 Jul 21, 2019
 #1
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The largest n = 164

 Jul 21, 2019
 #2
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Because, if you fator 1000!, you will see that 7^164 is one of its factors.

Guest Jul 21, 2019
 #3
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What is the largest integer \(n\) such that \(7^n\) divides \(1000!\)

 

\(\text{The largest integer $= \left[\dfrac{1000}{7}\right] + \left[\dfrac{1000}{7^2}\right] + \left[\dfrac{1000}{7^3}\right] \qquad [\ldots] =$ integer part. } \\ \text{The largest integer $= 142 + 20 + 2 $} \\ \text{The largest integer $= 164 $} \)

 

laugh

 Jul 22, 2019

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