Latest Infosys Aptitude Question SOLUTION: Find the maximum value of n such that 50! is perfectly divisible by 2520^n.

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Find the maximum value of n such that 50! is perfectly divisible by 2520^n.

Asked In Infosys Subrata Patra (10 years ago)

Solved RAKESH Read Solution (8)

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RAKESH  (10 years ago)

qn should be
Find the maximum value of n such that 50! is perfectly divisible by 2520^n .

ans: n(max)= 8

2520 = 2^3*3^2*5*7
Here, 7 is the highest prime,so find the no. of 7's in 50! only

no. of 7's in 50! = [50/7] + [50/7^2] = 7+1 = 8

for n(max)=8, 50! is perfectly divisible by 2520^8.

Is this solution Helpfull? Yes (57) | No (1)  

tirupathi reddy  (9 years ago)

Rakesh can u explain why we have to taken no of 7 in 50!

Is this solution Helpfull? Yes (6) | No (1)  

vicky  (9 years ago)

by RAHUL SAHA...(HIT)
2520=2^3*3^2*5*7
50/7+50/49=8
ans=8

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Anjusha Joshi  (10 years ago)

6!
6*5*4*3*2*1=720

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tirupathi reddy  (10 years ago)

n=1
see this method
10 fact/110n, by solving we get 660/110 so it is exactly divisible.
n*(n+1)/2= 10*11/2

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Rajdeep Chatterjee  (9 years ago)

I think the question is wrong..........

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prachi  (6 years ago)

answer should be 8

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Sourav Nayak  (2 years ago)

Video Solution
https://youtu.be/mfFqvdv4EYs

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