113967 ÷ 61 
Our goal is to divide 113967 by 61.

Step 1:
61 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 61

On to step 2:
If we divide 11 by 61, we get 0 and a remainder of 11.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 11 after subtracting 0 from 11.
Include the next digit (3) from the dividend after 11, then repeat: 113 / 61

Let's proceed to step 3:
The number 61 fits into 113 1 times, leaving a remainder of 52.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 61 from 113 leaves us with 52.
Take the next digit (9) from the dividend and append it to 52, then repeat: 529 / 61

Going ahead to step 4:
When dividing 529 by 61, we get 8 with a remainder of 41.
The next digit of our result is 8. 
Result so far: 18.0
If we subtract 488 from 529, we get 41.
Grab the next digit (6) from the dividend, add it to 41, then carry on: 416 / 61

Going ahead to step 5:
If we divide 416 by 61, we get 6 and a remainder of 50.
The next digit of our result is 6. 
Result so far: 186.0
If we subtract 366 from 416, we get 50.
Fetch the next digit (7) from the dividend, attach it to 50 and continue: 507 / 61

Going ahead to step 6:
The number 61 fits into 507 8 times, leaving a remainder of 19.
Put 8 as the next digit of the answer. 
Result so far: 1868.0
Subtract 488 from 507 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 7:
61 can be fit into 190 3 times, resulting in a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 1868.3
Deduct 183 from 190 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 8:
If we divide 70 by 61, we get 1 and a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 1868.31
Subtracting 61 from 70 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
When dividing 90 by 61, we get 1 with a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 1868.311
Subtracting 61 from 90 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

After the division, we end up with 1868.311 and a remainder of 0.0029.