Question

Find the remainder when ${357}^{678}$ is divided by 25?

• A. 49
• B. 19
• C. 24
• D. 4

Answer 1

The correct option is C 24

${357}^{678}=({357}^4{)}^{169}\times ({357}^2)$
This can be re-written as,
$({57}^4{)}^{169}\times ({57}^2)$
since we are concerned only with the last two digits.
Now, $({57}^2\times {57}^2{)}^{169}\times ({57}^2)$
$=(49\times 49{)}^{169}\times 49$
$=(01{)}^{169}\times 49$
$=01\times 49=49$
Finally, 49 when divided by 25 will leave a remainder of 24.