The least remainder when 17^ 30 is divided by 5 is - Vidyadip

Question

The least remainder when ${17^{30}}$ is divided by $ 5$ is

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Answer

d
(d) $17 = 2$ (mod $5$) ${(17)^5} = {(2)^5}\,({\rm{mod 5)}}$ $= 2$ (mod $5$)

==> ${({17^5})^6} = {(2)^6}$(mod $5$)

==> ${(17)^{30}} = 4$ (mod $5$)Hence required remainder $= 4.$

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