India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

The remainder when 75^75⁷⁵ is divide by 37.

10
21
35
47

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{75^{75^{75}}}{37} \\ When 75 is divided by 37, it leaves remainder of 1. \\ So, the expression will become, \\ \frac{1^{75^{75}}}{37} \\ Now, for any power of 1, \\ we always get 1 and expression becomes, \\ \frac{1}{37} that leaves remainder 1 \end{aligned}

$\eqalign{ & \frac{{{{75}^{{{75}^{75}}}}}}{{37}} \cr & {\text{When 75 is divided by 37, it leaves remainder of }}1. \cr & {\text{So, the expression will become}}, \cr & \frac{{{1^{{{75}^{75}}}}}}{{37}} \cr & {\text{Now,}}\,{\text{for}}\,{\text{any}}\,{\text{power}}\,{\text{of}}\,1, \cr & {\text{we}}\,{\text{always}}\,{\text{get}}\,{\text{1}}\,{\text{and}}\,{\text{expression}}\,{\text{becomes}}, \cr & \frac{1}{{37}}\,{\text{that}}\,{\text{leaves}}\,{\text{remainder}}\,1 \cr}$

Workspace Report

Post your Comments

", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{75^{75^{75}}}{37} \\ When 75 is divided by 37, it leaves remainder of 1. \\ So, the expression will become, \\ \frac{1^{75^{75}}}{37} \\ Now, for any power of 1, \\ we always get 1 and expression becomes, \\ \frac{1}{37} that leaves remainder 1 \end{aligned}

$\eqalign{ & \frac{{{{75}^{{{75}^{75}}}}}}{{37}} \cr & {\text{When 75 is divided by 37, it leaves remainder of }}1. \cr & {\text{So, the expression will become}}, \cr & \frac{{{1^{{{75}^{75}}}}}}{{37}} \cr & {\text{Now,}}\,{\text{for}}\,{\text{any}}\,{\text{power}}\,{\text{of}}\,1, \cr & {\text{we}}\,{\text{always}}\,{\text{get}}\,{\text{1}}\,{\text{and}}\,{\text{expression}}\,{\text{becomes}}, \cr & \frac{1}{{37}}\,{\text{that}}\,{\text{leaves}}\,{\text{remainder}}\,1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

Test

Classes

E-Book