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5^99 is divided by 13 then remainder is

Answers (2)

We should try and reduce the numerator in this case. Let us have a look at the method below.

Remainder [5^99 / 13]

= Remainder [5*5^98 / 13]

= Remainder [5*25^49 / 13]

= Remainder [5*(-1)^49 / 13]

= Remainder [(-5) / 13]

= 8

Posted by

Satyajeet kumar

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It simply follows a cycle..

5^1 / 13  - Remainder is 5
5^2 / 13  - Remainder is 12
5^3 / 13  - Remainder is 8
5^4 / 13  - Remainder is 1

5^5 / 13  - Remainder is 5
5^6 / 13  - Remainder is 12

.......... and so on. Hence,

5^96 / 13  - Remainder is 1
5^97 / 13  - Remainder is 5
5^98 / 13  - Remainder is 12
5^99 / 13  - Remainder is 8

\frac{99}{4}\rightarrow remainder\ is \ 3

5^3/13 \rightarrow remainder\ is \ 8


Answer : 8

Posted by

sudhir.kumar

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