125670 ÷ 21 
Our goal is to divide 125670 by 21.

On to step 1:
When dividing 1 by 21, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 21

Step 2:
If we divide 12 by 21, we get 0 and a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 12 after subtracting 0 from 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 21

Step 3:
21 can be fit into 125 5 times, resulting in a remainder of 20.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 105 away from 125, we end up with 20.
Fetch the next digit (6) from the dividend, attach it to 20 and continue: 206 / 21

On to step 4:
The number 21 fits into 206 9 times, leaving a remainder of 17.
Put 9 as the next digit of the answer. 
Result so far: 59.0
Subtract 189 from 206 to get 17.
Take the next digit (7) from the dividend and append it to 17, then repeat: 177 / 21

Step 5:
If we divide 177 by 21, we get 8 and a remainder of 9.
Write down 8 as next digit of the result. 
Result so far: 598.0
Subtract 168 from 177 to get 9.
Include the next digit (0) from the dividend after 9, then repeat: 90 / 21

On to step 6:
When dividing 90 by 21, we get 4 with a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 5984.0
Subtracting 84 from 90 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
When dividing 60 by 21, we get 2 with a remainder of 18.
Put 2 as the next digit of the answer. 
Result so far: 5984.2
The remainder is 18 after subtracting 42 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 8:
21 goes into 180 8 times with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 5984.28
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
21 can be fit into 120 5 times, resulting in a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 5984.285
Subtract 105 from 120 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 10:
If we divide 150 by 21, we get 7 and a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 5984.2857
Subtracting 147 from 150 leaves us 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.

Let's proceed to step 11:
30 divided by 21 is 1 with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 5984.28571
Subtract 21 from 30 to 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 12:
When dividing 90 by 21, we get 4 with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 5984.285714
If we subtract 84 from 90, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 13:
The number 21 fits into 60 2 times, leaving a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 5984.2857142
If we subtract 42 from 60, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 14:
If we divide 180 by 21, we get 8 and a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 5984.28571428
The remainder is 12 after subtracting 168 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 5984.28571428 with a balance of 1.2e-08.