Let's divide 10642 by 61
Our goal is to divide 10642 by 61.

Advancing to step 1:
1 divided by 61 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 61

Going ahead to step 2:
When dividing 10 by 61, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Bring next digit (6) of the dividend behind the 10 and repeat the process: 106 / 61

Going ahead to step 3:
The number 61 fits into 106 1 times, leaving a remainder of 45.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 45 after subtracting 61 from 106.
Fetch the next digit (4) from the dividend, attach it to 45 and continue: 454 / 61

Advancing to step 4:
When dividing 454 by 61, we get 7 with a remainder of 27.
Use 7 as the next digit of our solution. 
Result so far: 17.0
The remainder is 27 after subtracting 427 from 454.
Take the next digit (2) from the dividend and append it to 27, then repeat: 272 / 61

Advancing to step 5:
61 goes into 272 4 times with a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 174.0
Subtract 244 from 272 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 6:
280 divided by 61 is 4 with a remainder of 36.
Record the quotient 4 as the next digit in the result. 
Result so far: 174.4
If we take 244 away from 280, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 7:
If we divide 360 by 61, we get 5 and a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 174.45
Deduct 305 from 360 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Going ahead to step 8:
550 divided by 61 is 9 with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 174.459
Subtracting 549 from 550 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 9:
The number 61 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 174.459
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 10:
The number 61 fits into 100 1 times, leaving a remainder of 39.
Write down 1 as next digit of the result. 
Result so far: 174.45901
Subtract 61 from 100 to get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Step 11:
When dividing 390 by 61, we get 6 with a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 174.459016
The remainder is 24 after subtracting 366 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 12:
When dividing 240 by 61, we get 3 with a remainder of 57.
The number 3 becomes the next digit in our result. 
Result so far: 174.4590163
If we subtract 183 from 240, we get 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Going ahead to step 13:
If we divide 570 by 61, we get 9 and a remainder of 21.
The next digit of our result is 9. 
Result so far: 174.45901639
If we subtract 549 from 570, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

In conclusion, the division gives 174.45901639 with a balance of 2.1e-08.