Hello, could somebody please explain how I find the rule for numbers divisible by 11?
Thanks

Do you want the rule or the proof? I'll write what the rule actually is for the meantime:

Suppose the number in question is:

ABCDEFGHI...

In other words its first digit is A, its second digit is B etc.

The rule is, if A - B + C - D + E - F + ... is divisible by 11, then so is the whole number.

For instance, 627. If you do the sum you get:

6 - 2 + 7 = 11

As 11 is divisible by 11 (11 = 1 x 11), 627 is divisible by 11 (and indeed 627 = 57 x 11).

Or consider 473

4 - 7 + 3 = 0

0 is divisible by 11 (0 = 0 x 11) so 473 is divisible by 11. 473 = 43 x 11.

On the other hand 67 which goes to 6 - 7 = -1 is not divisible by 11, so neither is 67.

• We want to test whether 733 is a multiply of 11. To do this we calculate:
  
  + 7 -3 + 3 (notice that we alternate between + and -and run through the digits of the number)
  
  This comes to 7. Now 7 is not a multiple of 11, so 733 is not a multiple of 11.
• Another one: 49256.
  
  + 4 -9 + 2 -5 + 6 = -2
  
  -2 is not a multiple of 11, so neither is 49256.
• Or: 7777777777777
  
  You get:
  
  + 7 -7 + 7 -7 + 7 -7 + 7- 7 + 7- 7 + 7- 7 + 7- 7 = 0
  
  Now 0 is a multiple of 11 (because 0 x 11 = 0) as is 77777777777777.
• Or 9141924:
  
  + 9- 1 + 4- 1 + 9- 2 + 4 = 22
  
  Now 22 is a multiple of 11, and so is 9141924.