Let's divide 126574 by 59
Our goal is to divide 126574 by 59.

On to step 1:
If we divide 1 by 59, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 59

On to step 2:
59 can be fit into 12 0 times, resulting in a remainder of 12.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 12 after subtracting 0 from 12.
Include the next digit (6) from the dividend after 12, then repeat: 126 / 59

Going ahead to step 3:
59 can be fit into 126 2 times, resulting in a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we subtract 118 from 126, we get 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 59

On to step 4:
59 goes into 85 1 times with a remainder of 26.
The next digit of our result is 1. 
Result so far: 21.0
If we subtract 59 from 85, we get 26.
Grab the next digit (7) from the dividend, add it to 26, then carry on: 267 / 59

Let's proceed to step 5:
267 divided by 59 is 4 with a remainder of 31.
Use 4 as the next digit of our solution. 
Result so far: 214.0
If we take 236 away from 267, we end up with 31.
Include the next digit (4) from the dividend after 31, then repeat: 314 / 59

Let's proceed to step 6:
59 can be fit into 314 5 times, resulting in a remainder of 19.
Write down 5 as next digit of the result. 
Result so far: 2145.0
Subtracting 295 from 314 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 7:
190 divided by 59 is 3 with a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 2145.3
Subtracting 177 from 190 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 8:
130 divided by 59 is 2 with a remainder of 12.
The next digit of our result is 2. 
Result so far: 2145.32
Subtract 118 from 130 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
120 divided by 59 is 2 with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 2145.322
Subtracting 118 from 120 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 2145.322, and the remainder is 0.0002.