125637 divided by 19 
Our goal is to divide 125637 by 19.

Advancing to step 1:
19 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 19

Advancing to step 2:
The number 19 fits into 12 0 times, leaving a remainder of 12.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 12 leaves us with 12.
Fetch the next digit (5) from the dividend, attach it to 12 and continue: 125 / 19

Advancing to step 3:
125 divided by 19 is 6 with a remainder of 11.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 114 from 125, we get 11.
Grab the next digit (6) from the dividend, add it to 11, then carry on: 116 / 19

Going ahead to step 4:
If we divide 116 by 19, we get 6 and a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 66.0
Deduct 114 from 116 and we're left with 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 19

Moving on to step 5:
23 divided by 19 is 1 with a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 661.0
If we subtract 19 from 23, we get 4.
Include the next digit (7) from the dividend after 4, then repeat: 47 / 19

Moving on to step 6:
The number 19 fits into 47 2 times, leaving a remainder of 9.
The next digit of our result is 2. 
Result so far: 6612.0
If we subtract 38 from 47, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 7:
When dividing 90 by 19, we get 4 with a remainder of 14.
Record the quotient 4 as the next digit in the result. 
Result so far: 6612.4
If we take 76 away from 90, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 8:
19 goes into 140 7 times with a remainder of 7.
Put 7 as the next digit of the answer. 
Result so far: 6612.47
Deduct 133 from 140 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 9:
The number 19 fits into 70 3 times, leaving a remainder of 13.
Use 3 as the next digit of our solution. 
Result so far: 6612.473
Deduct 57 from 70 and we're left 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.

Advancing to step 10:
The number 19 fits into 130 6 times, leaving a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 6612.4736
If we subtract 114 from 130, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 11:
19 can be fit into 160 8 times, resulting in a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 6612.47368
Subtracting 152 from 160 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 12:
The number 19 fits into 80 4 times, leaving a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 6612.473684
Deduct 76 from 80 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 13:
When dividing 40 by 19, we get 2 with a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 6612.4736842
The remainder is 2 after subtracting 38 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 14:
The number 19 fits into 20 1 times, leaving a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 6612.47368421
Deduct 19 from 20 and we're left 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.

Our division results in 6612.47368421 with a remaining 1e-09.