138821 ÷ 25 
We want to figure out the number of times 138821 can be divided by 25.

Advancing to step 1:
If we divide 1 by 25, we get 0 and 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.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 25

Let's proceed to step 2:
If we divide 13 by 25, we get 0 and a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 13 after subtracting 0 from 13.
Grab the next digit (8) from the dividend, add it to 13, then carry on: 138 / 25

Moving on to step 3:
If we divide 138 by 25, we get 5 and a remainder of 13.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 125 from 138 and we're left with 13.
Include the next digit (8) from the dividend after 13, then repeat: 138 / 25

Going ahead to step 4:
25 goes into 138 5 times with a remainder of 13.
Put 5 as the next digit of the answer. 
Result so far: 55.0
Deduct 125 from 138 and we're left with 13.
Include the next digit (2) from the dividend after 13, then repeat: 132 / 25

Advancing to step 5:
The number 25 fits into 132 5 times, leaving a remainder of 7.
Put 5 as the next digit of the answer. 
Result so far: 555.0
If we take 125 away from 132, we end up with 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 25

Advancing to step 6:
71 divided by 25 is 2 with a remainder of 21.
The next digit of our result is 2. 
Result so far: 5552.0
Subtracting 50 from 71 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Step 7:
25 goes into 210 8 times with a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 5552.8
Subtracting 200 from 210 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.

Let's proceed to step 8:
25 goes into 100 4 times with a remainder of 0.
Write down 4 as next digit of the result. 
Result so far: 5552.84
Deduct 100 from 100 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.

On to step 9:
0 divided by 25 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 5552.84
Subtracting 0 from 0 leaves us 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 10:
If we divide 0 by 25, we get 0 and a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 5552.84
If we take 0 away from 0, 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.

After the division, we end up with 5552.84 and a remainder of 0.0.