Question

Q. What is the reminder when $3^{35}$ is divided by 7?

• A. 4
• B. 6
• C. 5
• D. 3
• E. 2

Answer 1

The correct option is C 5

$Rem\left(\frac{3^{35}}{7}\right)=Rem\frac{(3^2{)}^{17}\times 3^1}{7}=Rem(\frac{2^{17}}{7}\times \frac{3}{7})=Rem(\frac{(2^3{)}^5}{7}\times \frac{2^2}{7}\times \frac{3}{7})=Rem(1^5\times \frac{12}{7})=5$