Question 83

If n is the largest positive integer such that $$7^n$$ divides $$(68)!$$, then n =

Solution

The largest power of 7 that divides $$(68)!$$ = Sum of the quotients of {$$\frac{68}{7}$$, $$\frac{68}{7^2}$$, $$\frac{68}{7^3}$$, .......}

= Sum of the quotients of {$$\frac{68}{7}$$, $$\frac{68}{49}$$, $$\frac{68}{343}$$, .......}

= 9 + 1 + 0 + 0 + .....

= 10

$$\therefore\ $$n = 10

Hence, the correct answer is Option B

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