We're dividing 137920 by 25 
We're looking to find how many times 25 goes into 137920.

On to step 1:
25 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 25

Step 2:
25 can be fit into 13 0 times, resulting in a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 13 after subtracting 0 from 13.
Fetch the next digit (7) from the dividend, attach it to 13 and continue: 137 / 25

Let's proceed to step 3:
If we divide 137 by 25, we get 5 and a remainder of 12.
Put 5 as the next digit of the answer. 
Result so far: 5.0
If we subtract 125 from 137, we get 12.
Bring next digit (9) of the dividend behind the 12 and repeat the process: 129 / 25

Let's proceed to step 4:
When dividing 129 by 25, we get 5 with a remainder of 4.
Write down 5 as next digit of the result. 
Result so far: 55.0
Subtract 125 from 129 to get 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 25

Going ahead to step 5:
The number 25 fits into 42 1 times, leaving a remainder of 17.
The number 1 becomes the next digit in our result. 
Result so far: 551.0
If we take 25 away from 42, we end up with 17.
Grab the next digit (0) from the dividend, add it to 17, then carry on: 170 / 25

Step 6:
When dividing 170 by 25, we get 6 with a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 5516.0
If we take 150 away from 170, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 7:
200 divided by 25 is 8 with a remainder of 0.
Write down 8 as next digit of the result. 
Result so far: 5516.8
If we take 200 away from 200, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
0 divided by 25 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 5516.8
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 9:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 5516.8
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 5516.8 with a remainder of 0.0.