Question

2^35 divided by 5 remainder ?

Answer 1

2^(4×8+3) ÷ 5 = 2^(4×8) ×2³ ÷ 5
= (16)^8 × 8 ÷ 5
16^8 ÷ 5 remainder is 1
8/5 remainder is 3

Remainder = 1×3 = 3

Answer 2

3 is the remainder when $2^{35}$ divided by 5.

Given:

$2^{35}$ divided by 5

To find:

Remainder = ?

Solution:

To find the remainder of$2^{35},$

Let us reconstruct the power of 2 in such a way that it is easy to solve, now as we can see that the power of 2 is 35, so to easily solve the division we are going to deconstruct the power 35 into $(4 \times 8 + 3)$ which means dividing

$(4 \times 8 + 3)$ by 3, we get$\left(\frac{4 \times 8}{3}+\frac{3}{3}\right)$which means the remainder will be$\left(\frac{4 \times 8}{3}+\frac{3}{3}\right) =(2+1)=3.$

Therefore, the remainder is 3.