Let me explain this rule by taking examples
consider number 34568276, we have to calculate the reminder on diving this number by 7 11 and 13 respectively.
make triplets as written below starting from units place
34.........568..........276
now alternate sum = 34+276 = 310 and 568
and difference of these sums = 568-310 = 258
divide it by 7 we get reminder as 6
divide it by 11 we get reminder as 5
divide it by 13 we get reminder as 11
Other Example-
consider the number 4523895099854
triplet 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 reminder as 4
divide it by 11 we get reminder as 9
divide it by 13 we get reminder as 0
