Take the number to be divided by 11 and starting from the last two digits and going on to the beginning, separate it into groups of two digits. If you finally turn up with one digit, keep that instead. Add the groups of digits you have found in normal decimal division, and continue the process until you are left with a two-digit number. If the two-digit number is divisible by 11, so was the initial number, else the remainder of the division by 11 of the two-digit number is the remainder of the division by 11 of the initial number.
Example: Take 1771561. Taking two-digit groups from the end to the beginning, we have: 61+15+77+1=154. 54+1=55. So this number is exactly divisible by 11.
Another example: Take 987654321. Taking two-digit groups from the end to the beginning, we have 21+43=64. 64+65=129. 129+87=216. 216+9=225. 2+25=27, so this number gives a remainder of 5 when divided by 11.
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