135821 ÷ 10 
We're looking to find how many times 10 goes into 135821.

Going ahead to step 1:
If we divide 1 by 10, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 10

Let's proceed to step 2:
When dividing 13 by 10, we get 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 10 from 13 and we're left with 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 10

Advancing to step 3:
The number 10 fits into 35 3 times, leaving a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtract 30 from 35 to get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 10

Advancing to step 4:
10 can be fit into 58 5 times, resulting in a remainder of 8.
Write down 5 as next digit of the result. 
Result so far: 135.0
The remainder is 8 after subtracting 50 from 58.
Fetch the next digit (2) from the dividend, attach it to 8 and continue: 82 / 10

Advancing to step 5:
10 can be fit into 82 8 times, resulting in a remainder of 2.
The next digit of our result is 8. 
Result so far: 1358.0
The remainder is 2 after subtracting 80 from 82.
Grab the next digit (1) from the dividend, add it to 2, then carry on: 21 / 10

Let's proceed to step 6:
10 goes into 21 2 times with a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 13582.0
Subtracting 20 from 21 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
10 can be fit into 10 1 times, resulting in a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 13582.1
Subtract 10 from 10 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.

Step 8:
10 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: 13582.1
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.

Step 9:
The number 10 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 13582.1
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.

Our division results in 13582.1 with a remaining 0.0.