Question

What will be the remainder if $2^{89}$ is divided by 9?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer:

D. 5

$(2^{89}/9)$

$⇒ \frac{(2^3)^29 × 2^2}{9}$

$⇒ \frac{(8)^29 \times{4}}{9}$

$⇒\frac{(-1)^29 × 4}{9}$

$⇒ \frac{(-1\times{4})}{9}$

$⇒\frac{ - 4}{9}$

⇒ Remainder = - 4 + 9 = 5