Casting Out Elevens is a slightly slower but more accurate way to sanity check your work. It is a great way to catch most errors including digit reversals (transposing two digits).
Casting Out Elevens can be used when dividing numbers of any size.
Step 1
Find the digit sum for each number being divided and for the answer.
540 digit sum is 1
36 digit sum is 3
15 digit sum is 4
Step 2
Multiply the digit sum of the division problems answer by the digit sum of number you are dividing by.
3 x 4 = 12
Step 3
Find the digit sum of the answer in Step 2.
12 digit sum is 1
Step 4
The division problems answer is probably correct if the digit sum found in Step 3 and the digit sum of the number being divided are the same.
1 = 1 so 15 is probably correct.
Remainders
For division problems with remainders simply subtract the remainder from the number being divided before proceeding with the rest Casting Out Elevens for division check.
543 / 36 = 15 Remainder 3
543 - 3 = 540
So, the problem becomes 540 / 36 = 15 for the Casting Out Elevens check.