Question

Find remainder when 382382...up to 300 digit is divided by 101

Answer 1

Answer:

remainder = 0

Step-by-step explanation:

Mark off the number in groups of two digits starting from the right, and add the two-digit groups together with alternating signs. If the sum is divisible by 101 then the original number is also divisible by 101.

382382382..................................................................382382382

Total 300 digit

100 groups of 382

(82 + 38 + 23 + 82 + 38 + 23 +...............)  - (23 + 82 + 38 +..................)

= 25 * (82 + 38 + 23) -  25* (23 + 82 + 38)

= 0

Hence number is divisible by 101

so remainder = 0