Binomial TheoremHard
Question
The largest $n \in N$, for which $7^{n}$ divides 101!, is :
Options
A.16
B.18
C.15
D.19
Solution
Exponent of 7 in 101 !
$${= \left\lbrack \frac{101}{7} \right\rbrack + \left\lbrack \frac{101}{7^{2}} \right\rbrack + \left\lbrack \frac{101}{7^{3}} \right\rbrack + \ldots\ldots }{= 14 + 2 = 16}$$
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