Let's divide 125974 by 78
We want to divide 125974 by 78.

Advancing to step 1:
The number 78 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 78

Let's proceed to step 2:
78 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
Subtract 0 from 12 to get 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 78

Let's proceed to step 3:
78 can be fit into 125 1 times, resulting in a remainder of 47.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 78 from 125 leaves us with 47.
Grab the next digit (9) from the dividend, add it to 47, then carry on: 479 / 78

On to step 4:
The number 78 fits into 479 6 times, leaving a remainder of 11.
The next digit of our result is 6. 
Result so far: 16.0
Deduct 468 from 479 and we're left with 11.
Fetch the next digit (7) from the dividend, attach it to 11 and continue: 117 / 78

Going ahead to step 5:
The number 78 fits into 117 1 times, leaving a remainder of 39.
Put 1 as the next digit of the answer. 
Result so far: 161.0
If we take 78 away from 117, we end up with 39.
Take the next digit (4) from the dividend and append it to 39, then repeat: 394 / 78

Step 6:
When dividing 394 by 78, we get 5 with a remainder of 4.
Record the quotient 5 as the next digit in the result. 
Result so far: 1615.0
If we take 390 away from 394, we end up 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 7:
78 goes into 40 0 times with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 1615.0
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 8:
400 divided by 78 is 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 1615.05
The remainder is 10 after subtracting 390 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 9:
If we divide 100 by 78, we get 1 and a remainder of 22.
The next digit of our result is 1. 
Result so far: 1615.051
Deduct 78 from 100 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 10:
When dividing 220 by 78, we get 2 with a remainder of 64.
Write down 2 as next digit of the result. 
Result so far: 1615.0512
Subtracting 156 from 220 leaves us with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Advancing to step 11:
If we divide 640 by 78, we get 8 and a remainder of 16.
The next digit of our result is 8. 
Result so far: 1615.05128
Subtracting 624 from 640 leaves us with 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 12:
78 can be fit into 160 2 times, resulting in a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 1615.051282
Deduct 156 from 160 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.

Moving on to step 13:
The number 78 fits into 40 0 times, leaving a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 1615.051282
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 14:
78 goes into 400 5 times with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 1615.05128205
Subtracting 390 from 400 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 1615.05128205 with a balance of 1e-08.