Greatest Possible Positive Integer
What is the greatest possible positive integer n if 8^n divides (44)^44 without leaving a remainder?
Answers
Answered by
3
Ans:44^44 = 2^88 *11^44
= 8^29 * 2 * 11^44
so ans is 29
= 8^29 * 2 * 11^44
so ans is 29
Answered by
1
Answer:
We can write the value of 44^44 from the given equation in the form of the integers such as breaking the 44^44 in (4*11)^4 or 4^44*11^44 or this can also be written as 4^(2*22)*11^44 or 16^22 * 11^44 or can be (2*8)^22*11^44 hence can be written as 2^22*8^22*11^44 .
Now we know the reduced form of the given data if we divide the value of 8^n we will get that the value of n will be 22 so that the total value will be 2^22*11^44. Hence, the value of the n will be 22.
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