Question

The remainder when $5^{99}$ is divided by $13$, is?

• A. $6$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (B)

$8$

$5^1$ / 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
......we observe a pattern. 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

correct answer is (b) 8