Trick to find divisibility by 7,13,17,19,23,29.

A trick to find out the divisibility by 7,13,17,19,23,29 using check multipliers.

The trick:
step 1:Multiply the units digit by the check multiplier then add this to the original number after removing its tens digit.
step2:Check if this new number is divisible by our number if not then you can again do step 1.This can be done until the number is reduced to a number which can be easily said to be divisible by our number.

Finding check multiplier:
If we want to find the check multiplier for 13: Multiply 13 to get the units digit as 9. In this case 13*3 = 39.So the check multiplier is +1 the tens digit i.e 3+1 = 4.
The trick is to get the units digit as 9. This can be used even for 7 where 7*7=49 so the check multiplier is 5.

Checking with examples:
Is 169 divisible by 13?
First find the check multiplier for 13 = 13*3 = 39 = 3+1 = 4.
9*4 = 36 (multiply the units digit with the check multiplier. )
36+16 = 52 (Add 36 to 16.16 is obtained by removing the units digit from 169.)
Now we know 52 is a multiple of 13. So 169 is divisible by 13. If you are not sure if 52 is divisible by 13 then reduce 52 again. 5+2*4 =13. Now 13 is divisible by13! :-D

This same trick can be used for numbers like 7,17,19,23,29. For these numbers also try to get the units digit as 9 and hence the check multiplier.

Please let me know how you like this trick. I got this from a vedic maths book.