We're dividing 638290 by 61 
We want to figure out the number of times 638290 can be divided by 61.

Moving on to step 1:
The number 61 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 61

Step 2:
If we divide 63 by 61, we get 1 and a remainder of 2.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 2 after subtracting 61 from 63.
Grab the next digit (8) from the dividend, add it to 2, then carry on: 28 / 61

Going ahead to step 3:
The number 61 fits into 28 0 times, leaving a remainder of 28.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we subtract 0 from 28, we get 28.
Include the next digit (2) from the dividend after 28, then repeat: 282 / 61

Advancing to step 4:
282 divided by 61 is 4 with a remainder of 38.
The number 4 becomes the next digit in our result. 
Result so far: 104.0
If we subtract 244 from 282, we get 38.
Grab the next digit (9) from the dividend, add it to 38, then carry on: 389 / 61

Step 5:
When dividing 389 by 61, we get 6 with a remainder of 23.
Write down 6 as next digit of the result. 
Result so far: 1046.0
Subtract 366 from 389 to get 23.
Take the next digit (0) from the dividend and append it to 23, then repeat: 230 / 61

On to step 6:
If we divide 230 by 61, we get 3 and a remainder of 47.
The next digit of our result is 3. 
Result so far: 10463.0
Subtracting 183 from 230 leaves us with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

On to step 7:
The number 61 fits into 470 7 times, leaving a remainder of 43.
Put 7 as the next digit of the answer. 
Result so far: 10463.7
If we subtract 427 from 470, we get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Advancing to step 8:
430 divided by 61 is 7 with a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 10463.77
Deduct 427 from 430 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The quotient of the division is 10463.77, and the remainder is 0.003.