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# Help is needed

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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

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The largest n = 164

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

Guest Jul 21, 2019
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What is the largest integer $$n$$ such that $$7^n$$ divides $$1000!$$

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

Jul 22, 2019