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!

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.

That's pretty interesting. Does the book also say how exactly this works? What are the properties of the numbers that allow this system to be applied?
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Hi, I'm DonQuixote, a former GMAT Pill student who scored 780. I'm very grateful for this score and have now joined their staff My account of my GMAT experience can be found here.

I want to make a comment that as far as the GMAT is concerned, these divisibility rules are completely irrelevant. Now if you would like to have fun with divisibility, then that is a different story. Almost all of the divisions on the GMAT are very basic, and the goal of the test writers is not to test a student's ability to crunch numbers rapidly.

Cheers,
Dabral
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