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When expressed in base 8, N! terminates in a block of exactly 21 zeros. Find the largest positive integer N with this property. (Express N as a decimal number.)

 

(I got 159, but this is wrong.)

 May 2, 2020
edited by MathCuber  May 2, 2020
 #1
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+1

N = 66 in base 10.  If you convert it to base 8 =102 and 102! ends in 21 zeros.

 May 2, 2020
 #2
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Wouldn't it be the smallest positive integer N that you are looking for?

 May 2, 2020
 #3
avatar+8 
+1

67, wrote python to do it. Also u in my aops class right? who r u? cheater

 


def TrailingZeros(n): 
    
    
    count = 0


    i=2
    while (n/i>=1): 
      
      
        count += int(n/i) 
        i *= 2

    return int(count) 


n = 66

print(TrailingZeros(n)//3) 


 

 May 4, 2020

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