Question

the remainder when 7^905 is divided by 48​

Answer 1

Answer:

7905 is divided by 48 then answer will be 165.625

by round off the anwer is 165.6

Answer 2

Given:

Number given is $7^{905}$

To Find:

Remainder of $\frac{7^{905}}{48}$

Solution:

Applying Remainder Theorem,

$49=1 mod(48)$

$7^{2}=1 mod(48)$

$(7^{2})^{452}=1^{452}mod(48)$

$7^{904}=1mod(48)$.........................(1)

$7=-7mod(48)$...........................(2)

Multiplying eq (1) and eq(2), we get

$7^{905}=-7mod(48)$

$7^{905}=41mod(48)$

Hence the remainder is 41.