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

0

100 bottles of wine is sold by an innkeeper in 8 days, each day overpassing by 3 bottles the qty sold on the previous day. How many bottles did he sell on the first day ?

0

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

in a school there were some students. at annual function of the school if each student given one rupee more than the number students in the school, then total rupee collected was 444222. how many students in the school?

0

5^134/140 find remainder

0

Find the remainder when 47^57^67 is divided by 18?

by euler Re(47^6/18) =1
hence (47^(6k+R))/18 = (47^R)/18 ........(1)
Where R is remainder when 57^67 is divided by 6
so R is Re(57^67)/6 = (3^67)/6 = 3
so now
putting value of R is equation (1)
answer is (47^3)/18 = (11^3)/18 = 121*11/18 = 13.*11/18 = 143/18 = 17

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