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What is the greatest possible positive integer n if 16^n divides (44)^44 without leaving a remainder
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- (44)^44 = (4 × 11)^44 = (4^44) x (11^4) = ((4^2)^22) x (11^4) = (16^22) x (11^4). Therefore n=22. Answer
- 6 years agoHelpfull: Yes(5) No(4)
- please clearly tell me the solution for this que...
- 6 years agoHelpfull: Yes(2) No(0)
- 44^44=(2^88)*(11^44)
16^n=2^(4n)
n=22 - 6 years agoHelpfull: Yes(2) No(1)
- (44)^44=(4*11)^44
=(4)^44*(11)^44
=(2^2)^44*(11)^44
=(2)^88*(11)^44.
Now come to the denominator
(2^4)^n
=(2)^4n
ie. ((2^88)*(11^44))/(2^4n)
So,4n=88
n=22
Ans:22 - 3 years agoHelpfull: Yes(1) No(0)
- 2 is the possible positive integer
- 6 years agoHelpfull: Yes(0) No(4)
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