Question

find the remainder when 7^150 is divided by 4

Answer 1

ANSWER

1

SOLUTION

=> 7^150 = (8-1)^(150)

=> From binomial expansion

=> (8-1)^(150) can be written in the form of

8k+1 ....... { see attachment }

Hence overall number will be in the form of 8k+1 and all terms can be divided by 4 except last term

last term is 1

so remainder is 1

special note

for example if 5 is divided by 4 it leaves remainder 1 . 5 (example) can be written as 4k+1 ( k = natural number)

from binomial expansion we can say that 5^(150) is of the form of 4k+1 and leave remainder 1.

hope it helps

Answer 2

Answer:

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