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Easiest way to Find the Remainder on dividing by 7

Debraj Paul
22/03/2017 0 0

Split the digits of the number in a group of 3 starting from unit’s place. Add the alternate group and then find their difference. Divide the difference by 7 and get the remainder.

Consider the number 43456827. 

Make triplets as written below starting from unit’s place
43.........456..........827
Now alternate sum = 43 + 827=870 and 456 and difference of these sums = 870 - 456 = 414. Divide it by 7 we get remainder as 1.

Another example, consider the number 4523895099854

Triplets pairs are 4…523…895…099…854

Alternate sums are 4 + 895 + 854 = 1753 and 523 + 099 = 622.

Difference =1131

Revise the same tripling process 1…131

So, difference = 131-1=130 

Divide it by 7 we get remainder as 4.

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