Question

solution plzz... (5^625)/7[find Remainder]​

Answer 1

Answer:

5

Step-by-step explanation:

Solution is based on a repetitive pattern and this is how it goes….

5^1 = 5 so 5/7 will give you 5 as remainder.

5^2 = 25 so 25/7 will give you 4 as remainder.

5^3 = 125 so 125/7 will give you 6 as remainder.

5^4 = 625 so 625/7 will give you 2 as remainder.

5^5 = 3125 so 3125/7 will give you 3 as remainder.

5^6 = 15625 so 15625/7 will give you 1 as remainder.

5^7 = 78125 so 78125/7 will give you 5 as remainder.

5^8 = 390625 so 390625/7 will give you 4 as remainder.

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from above calculations we can see that the remainder pattern (5,4,6,2,3,1,5,4,……) keeps on repeating after every six numbers.

Thus the remainder on 5^1 = remainder of 5^7 = remainder of 5^13 and so on…..

Hence, dividing 625 by 6 (as the pattern repeats after every six numbers) we get 1 as the remainder and thus the first digit in the pattern and our final answer to the question is FIVE.

Incase,

if the question is 5^626; then the remainder of 626 / 6 = 2, then the 2nd digit of the pattern would have been the answer i.e. 4

I hope this clarifies.