Question

find the remainder when 2^11 is divided by 5

Answer 1

Answer:

$\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times2 }{5} = \\ \frac{2048}{5}$

Step-by-step explanation:

remainder is 3

Answer 2

After $2^4$ the unit digit repeats

$\frac{2^1^1}{5}=\frac{(2^4)^2\times2^3}{5}\\ =\frac{2^4^k\times2^3}{5}$

Write only unit place

$\frac{2^1^1}{5}=\frac{6\times8}{5}$

$=\frac{48}{5}$

On dividing $48$ by $5,$ remainder is $3.$