Find the remainder when 230330 is divisible by 7

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answer is A.

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Detailed Solution

Concept- In this particular question, simplify the equation first so that the power is only a single digit integer, then divide this digit, square of digit, and cube of digit by specified divisor and look for a pattern to determine the answer.
Number given: 230330
Finding the residual after this is divided by 7 is now our task.
Now that we are aware of ax (b x) = a (b x), we can utilize this characteristic to solve for 230330=2(330) = 630 in the equation above.
Now as we know that when 6 is divided by 7 the remainder is 6.
Now when 62 is divide by 7 the remainder is

= 627 = 367

, remainder is 1
Now when 63 is divide by 7 the remainder is

= 637 = 2167

, remainder is 6
Now when 64 is divide by 7 the remainder is

= 647 = 12967

, remainder is 1
So, as we see that remainder is either 1 or 6 when divisible by 7.
Now as we see that when the power of 6 is odd the remainder is 6 and when the power of 6 is even the remainder is 1.
Hence, the correct answer is 1) 1

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