ABOUT DIVISIBILITY BY 11 AND 13

From a previous post, the rules for divisibility by 11 and 13 are:

11

Alternately add and subtract the digits from left to right. (You can think of the first digit as being 'added' to zero.) If the result (including 0) is divisible by 11, the number is also. Example: to see whether 365167484 is divisible by 11, start by subtracting: [0+]3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11.

13

Delete the last digit from the number, then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number. Here are a couple of examples: 286 Add the first digit to zero, then subtract and add alternately. +2 -8 +6 = 0; zero is divisible by 11, and so is 286 (try it with your calculator). 715 +7 -1 +5 = 11, 11 is divisible by 11 and so is 715 try it with your calculator). 286 again Delete the 6, multiply by 9, subtract from 28. 28 - 54 = -26, -26 is divisible by 13, and so is 286 try it with your calculator). 715 again Delete the 5, multiply by 9. 71-45 = 26, 26 is divisible by 13, so is 715 try it with your calculator).