Latest self Aptitude Question SOLUTION: Find the maximum value of n such that 157! is perfectly divisible by 12^n

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Find the maximum value of n such that 157! is perfectly divisible by 12^n

Shradha Mittal (10 years ago)

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Ashutosh Anshu  (10 years ago)

12=2*2*3
157/3+157/9+157/27+157/81= 52+17+5+1 = 75 (answer)

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Ashutosh Anshu  (10 years ago)

@shradha - see 12 = 2*2*3 . therefor we get 75 when we divide by d factorials of 3. now dividing by d factorials of 2 we get.
157/2+157/4+157/8+157/16+157/32+157/64+157/128 = 152
now to find the solutions of this type of problem we need to take min(152,75)
and i.e 75 . that's y 75 is the correct answer.
again if you have 18^n = then 18 = 3*3*2 . again you have to check for both 2 and 3. and the minimum wil be the answer,
Got It ?? :) :) :)

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Shradha Mittal  (10 years ago)

@ ashutosh anshu if there is 18^n or 12600^n in place of 12^n..then what is the solution? actually i want to know why u use 3 instead of 2 or why u didnt use both 2 and 3?

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sachin chauhan  (7 years ago)

what if 157! is perfectly divisible by 18^n

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