Question

one which of the following is the remainder when 74power 100 is divided by 9​

Answer 1

Step-by-step explanation:

74¹⁰⁰/9

74/9 remainder be 2

74²/9 remainder be 4

74³/9 remainder be 8

74⁴/9 remainder be 7

74⁵/9 remainder be 5

74⁶/9 remainder be 1

{(74⁶)¹⁶×74⁴}/9

(74⁶)¹⁶ remainder be 1

74⁴ remainder be 7

1×7 hence remainder be 7

#666

Answer 2

Given:

To find the remainder when $\[{74^{100}}\]$ is divided by 9​

Solution:

Apply remainder theorem,

$\[ = \frac{{{{74}^{100}}}}{9}\]$

Dividing 74 by 9, the remainder will be 2,

$\[ = \frac{{{2^{100}}}}{9}\]$

$\[ = \frac{{{{\left( {{2^3}} \right)}^{33}} \times 2}}{9}\]$

$\[ = \frac{{{8^{33}} \times 2}}{9}\]$

Dividing 8 by 9, the remainder will be -1,

$\[ = \frac{{{{\left( { - 1} \right)}^{33}} \times 2}}{9}\]$

$\[ = \frac{{ - 2}}{9}\]$

Since remainder will never be a negative number.

Therefore the remainder is,

$\[\begin{array}{l} = - 2 + 9\\ = 7\end{array}\]$

Hence the remainder is 7.