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

• 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.
  
• 10 years agoHelpfull: Yes(57) No(1)
• Rakesh can u explain why we have to taken no of 7 in 50!
  
• 9 years agoHelpfull: Yes(6) No(1)
• by RAHUL SAHA...(HIT)
  2520=2^3*3^2*5*7
  50/7+50/49=8
  ans=8
  
• 9 years agoHelpfull: Yes(3) No(0)
• 6!
  6*5*4*3*2*1=720
  
  
• 10 years agoHelpfull: Yes(0) No(9)
• 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
• 10 years agoHelpfull: Yes(0) No(2)
• I think the question is wrong..........
• 9 years agoHelpfull: Yes(0) No(5)
• answer should be 8
• 6 years agoHelpfull: Yes(0) No(0)
• Video Solution
  https://youtu.be/mfFqvdv4EYs
• 2 years agoHelpfull: Yes(0) No(0)