Vedic / Quicker / Shortcut Math ⇒ Topic : Divisibility of a number by 11

Using 11 a number is divisible if difference sum of Even places and sum of odd places is Zero so divisible by 11.

Example: 1236431460/11= 112402860. (1+3+4+1+6)(odd places)-(2+6+3+4+0)(Even places)=0 andsum of odd and Even digit is equal so the number is divisible by 11.

Example: 513678/11= 46698.(5+3+7)(odd places)-(1+6+8)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

Example: 874720/11= 79520. (8+4+2)(odd places)-(7+7+0)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

Example: 697972/11= 63452. (6+7+7)(odd places)-(9+9+2)(Even places)=0 and sum of odd and Even digit is equal so the number is divisible by 11.

Example: 7972813805/11= 724801255. (7+7+8+3+0)(odd places)-(9+2+1+8+5)(Even places)=0 andsum of odd and Even digit is equal so the number is divisible by 11.

Note: So Before going to divisible by 10 any number, first check the condition of sum of odd and Even digit is equal and difference sum of Even places and sum of odd places is Zero is divisible by 10 .Than numbers is divisible by 10.

Rule: If the sums of digits at odd and even places are equal or differ 14 a number divisible by 11, then the number is also divisible by 11.
Ex.1. 3245682 : S1 = 3+4+6+2= 15 and 57 = 2+5+8= 15 As Si = S2, the number is divisible by 11.
Ex.2. 283712 :S1 = 2+3+1= 6 and S2 = 8+7+2 17. As S1 and S2 differ by 11 (divisible by 11), the number is also divisible by 11.
.Ex.3. 84927291658 : S1 = 8+9+7+9+6+8=47 and S2 = 4+2+2+1+5= 14 As (S1 - S2 =) 33 is divisible by 11, the number is also divisible by 11.