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