Dividing any Number by 11

The technique for dividing any number by 11 mentally is simply to reduce a complex division to a simple subtraction. You need to follow the steps below:

Step-1:   Copy the first (left) digit from the dividend as it is and you have the first answer digit. Subtract it from the next digit of dividend and you have the second answer digit. Using the same logic, subtract this second answer digit from the next adjacent digit to get the third answer digit and continue the step with the other digits.

Step-2:   Combine all except the last set of digit to get partial quotient. The last digit would be the Remainder, if there is a remainder.

Step-3:   If any answer digit in any place except the last digit results in negative; subtract it from 10 and subtract 1 from its left digit. If last set of digit which happens to be the remainder results in negative, add 11 to it and subtract 1 from the partial quotient to get the final quotient and final remainder.

The whole calculation can be done mentally at a very fast speed.

156 ÷ 11 =?

Step 1:   Copy the first (left) digit of the dividend as it is which is 1, and you have the first answer digit. ->1

The next one would be the next digit of dividend that is 5 minus this answer digit 1. So, 5 minus 1 is 4. ->1,4

The next answer digit would be the next digit of dividend which is 6 minus this answer digit 4 that is 6-4 = 2. But do not write 2 as quotient, because this would be the remainder.

Step 2:   Combine all except the last set of digit to get partial quotient that is 14. The last digit finding 2 is the Remainder.

Answer: Quotient 14, Remainder 2

25789 ÷ 11 =?

Start copying the first (left) digit of the dividend as it is which is 2, and you have the first answer digit. ->2

The next one would be the next digit of dividend that is 5 minus this answer digit 2. So, 5 minus 2 is 3. ->2,3

The next answer digit would be the next digit of dividend which is 7 minus this answer digit 3 that is 7-3=4. ->2,3,4

Now, using the same logic, the next answer digit would be 8 minus 4, which is again 4. ->2,3,4,4

Next one would be 9 minus 4 that is 5. But do not write down 5 as quotient, because this would be the remainder.

So, the answer would be 2344 with a remainder 5.

25784 ÷ 11 =?

Step 1:         2, 5-2, 7-3, 8-4, 4-4

Step 2:         Quotient: 2,3,4,4; Remainder 0

Answer: 2344 with ‘NO’ Remainder

25352 ÷ 11 =?

Step 1:         2, 5-2, 3-3, 5-0, 2-5

Step 2:         Partial Quotient: 2,3,0,5; Remainder: -3

Step 3:         Final Quotient: 2305-1; Final Remainder -3+11

Answer: Quotient 2304, Remainder 8

45062 ÷ 11 =?

Step 1:         4, 5-4, 0-1, 6+1, 2-7

Step 2:         Partial Quotient: 4,1,-1,7; Remainder: -5

Step 3:         Final quotient: 4097-1; final remainder: -5+11

Answer:        Quotient 4096, Remainder 6

68051 ÷ 11 =?

6, 8-6, 0-2, 5+2, 1-7

6,2,-2,7,-6 = 6,20-2,7,-6 = 6,1,8,7,-6

Final quotient (6187-1) and final remainder (-6+11)

Answer: Quotient 6186, Remainder 5

28250 ÷ 11 =?

Quotient: 2, 8-2, 2-6, 5-(-4), Remainder: 0-9

Q: 2,6,-4,9 = 2,6-1,10-4,9 = 2,5,6,9 and R = -9

Final quotient 2569-1 = 2568 and final remainder -9+11 = 2

Answer: Quotient 2568, Remainder 2