138637 ÷ 71 
We want to divide 138637 by 71.

Advancing to step 1:
1 divided by 71 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 71

Step 2:
71 can be fit into 13 0 times, resulting in a remainder of 13.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 13 after subtracting 0 from 13.
Bring next digit (8) of the dividend behind the 13 and repeat the process: 138 / 71

Going ahead to step 3:
The number 71 fits into 138 1 times, leaving a remainder of 67.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 67 after subtracting 71 from 138.
Fetch the next digit (6) from the dividend, attach it to 67 and continue: 676 / 71

Let's proceed to step 4:
71 can be fit into 676 9 times, resulting in a remainder of 37.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
Deduct 639 from 676 and we're left with 37.
Append the next digit (3) from the dividend to 37 and continue with: 373 / 71

Advancing to step 5:
If we divide 373 by 71, we get 5 and a remainder of 18.
The next digit of our result is 5. 
Result so far: 195.0
Subtracting 355 from 373 leaves us with 18.
Append the next digit (7) from the dividend to 18 and continue with: 187 / 71

Moving on to step 6:
If we divide 187 by 71, we get 2 and a remainder of 45.
Record the quotient 2 as the next digit in the result. 
Result so far: 1952.0
Subtracting 142 from 187 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 7:
71 can be fit into 450 6 times, resulting in a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 1952.6
The remainder is 24 after subtracting 426 from 450.
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 8:
When dividing 240 by 71, we get 3 with a remainder of 27.
Record the quotient 3 as the next digit in the result. 
Result so far: 1952.63
If we subtract 213 from 240, we get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 9:
When dividing 270 by 71, we get 3 with a remainder of 57.
The next digit of our result is 3. 
Result so far: 1952.633
The remainder is 57 after subtracting 213 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

The final result is 1952.633 with a remainder of 0.0057.