AP ICET 2016 Paper

Question : 89 of 200

Marks: +1, -0

If n is the largest positive integer such that

7^n

divides (68)!, then

n=

Validate

Solution:

68! = 1 × 2 × ....... 7 × ..... × 14 × ....... 21 × ....× 28 × ..... × 35 ×...... × 42 × ....... × 49 × ...... × 56 × ........ × 63 × ....... × 68
∴ n = Quotient (68 ÷ 7) + Quotient (68 ÷ 49 i.e

7^2

)
⇒ n = 9 + 1 = 10

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