We divide 10642 by 61
We're looking to find how many times 61 goes into 10642.

Let's proceed to step 1:
1 divided by 61 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 61

On to step 2:
If we divide 10 by 61, we get 0 and a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Include the next digit (6) from the dividend after 10, then repeat: 106 / 61

Going ahead to step 3:
If we divide 106 by 61, we get 1 and a remainder of 45.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 61 away from 106, we end up with 45.
Fetch the next digit (4) from the dividend, attach it to 45 and continue: 454 / 61

On to step 4:
454 divided by 61 is 7 with a remainder of 27.
Write down 7 as next digit of the result. 
Result so far: 17.0
Subtracting 427 from 454 leaves us with 27.
Include the next digit (2) from the dividend after 27, then repeat: 272 / 61

Let's proceed to step 5:
The number 61 fits into 272 4 times, leaving a remainder of 28.
Record the quotient 4 as the next digit in the result. 
Result so far: 174.0
The remainder is 28 after subtracting 244 from 272.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 6:
61 goes into 280 4 times with a remainder of 36.
Record the quotient 4 as the next digit in the result. 
Result so far: 174.4
If we subtract 244 from 280, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 7:
360 divided by 61 is 5 with a remainder of 55.
Write down 5 as next digit of the result. 
Result so far: 174.45
The remainder is 55 after subtracting 305 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 8:
61 goes into 550 9 times with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 174.459
The remainder is 1 after subtracting 549 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 9:
When dividing 10 by 61, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 174.459
If we subtract 0 from 10, we 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.

Advancing to step 10:
If we divide 100 by 61, we get 1 and a remainder of 39.
Use 1 as the next digit of our solution. 
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.

Going ahead to step 11:
The number 61 fits into 390 6 times, leaving a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 174.459016
Deduct 366 from 390 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 12:
61 goes into 240 3 times with a remainder of 57.
Record the quotient 3 as the next digit in the result. 
Result so far: 174.4590163
Subtract 183 from 240 to 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.

Let's proceed to step 13:
61 can be fit into 570 9 times, resulting in a remainder of 21.
The number 9 becomes the next digit in our result. 
Result so far: 174.45901639
Deduct 549 from 570 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

The final result is 174.45901639 with a remainder of 2.1e-08.