Divisibility and Re...
 

Divisibility and Remainders  

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Find the maximum value of n such that 50! is perfectly divisible by 12600 raised to the power n.

10?

12600= (2^3)* (3^2)*(5^2)*(7)

powers of 2 in 50! by successive division = 50+25+12+6+3+1= 97, hence power of 2^3 will be 97/3 = 32
same way powers of 3 = 16+5+1 = 22; powers of 3^2 = 11
powers of 5 = 10+2 = 12; powers of 5^2 = 6
powers of 7 = 7+1 = 8
from the above set since there are only 6 powers of 5^2 are available, hence maximum value of n can be 6 only

93 Answers
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the distance between place A and place B is 97 meters . A mad man start walking from place A towards place B. He walks 7 meters in first 3 mins and in next 3 mins returns 4 meters, if this pattern continues until the mad man reach place B, Then find time taken by him to reach place B.

0

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