We're dividing 137774 by 25 
We want to divide 137774 by 25.

Advancing to step 1:
When dividing 1 by 25, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 25

Let's proceed to step 2:
The number 25 fits into 13 0 times, leaving a remainder of 13.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 13 leaves us with 13.
Fetch the next digit (7) from the dividend, attach it to 13 and continue: 137 / 25

Advancing to step 3:
When dividing 137 by 25, we get 5 with a remainder of 12.
Put 5 as the next digit of the answer. 
Result so far: 5.0
If we take 125 away from 137, we end up with 12.
Take the next digit (7) from the dividend and append it to 12, then repeat: 127 / 25

On to step 4:
25 goes into 127 5 times with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 55.0
The remainder is 2 after subtracting 125 from 127.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 25

Step 5:
27 divided by 25 is 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 551.0
Subtracting 25 from 27 leaves us with 2.
Fetch the next digit (4) from the dividend, attach it to 2 and continue: 24 / 25

Let's proceed to step 6:
If we divide 24 by 25, we get 0 and a remainder of 24.
Put 0 as the next digit of the answer. 
Result so far: 5510.0
Deduct 0 from 24 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 7:
240 divided by 25 is 9 with a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 5510.9
The remainder is 15 after subtracting 225 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 8:
When dividing 150 by 25, we get 6 with a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 5510.96
The remainder is 0 after subtracting 150 from 150.
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 9:
If we divide 0 by 25, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 5510.96
Subtract 0 from 0 to 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.

Going ahead to step 10:
When dividing 0 by 25, we get 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 5510.96
Subtract 0 from 0 to 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.

After the division, we end up with 5510.96 and a remainder of 0.0.