Question

remainder of 3^30 when divided by 4​

Answer 1

Step-by-step explanation:

3³⁰ ÷ 4 = 3³⁰ ÷ (3+1)

let x =3 then

x³⁰ ÷ (x+1)

f(x)=x³⁰ , when divided by (x+1) remainder is f(-1)

f(-1) = -1³⁰= 1

remainder is 1

Answer 2

Given:

Remainder of $\[{3^{30}}\]$ when divided by 4​

Solution:

Simplify the given expression,

$\[ = \frac{{{3^{30}}}}{4}\]$

$\[ = \frac{{{{\left( {{3^2}} \right)}^{15}}}}{4}\]$

$\[ = \frac{{{9^{15}}}}{4}\]$

Apply remainder theorem,

$\[ = \frac{{{1^{15}}}}{4}\]$

$\[ = \frac{1}{4}\]$

Hence, the remainder will be 1.