145827 ÷ 21 
We're looking to find how many times 21 goes into 145827.

Step 1:
1 divided by 21 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (4) from the dividend after 1, then repeat: 14 / 21

Let's proceed to step 2:
If we divide 14 by 21, we get 0 and a remainder of 14.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 14 after subtracting 0 from 14.
Fetch the next digit (5) from the dividend, attach it to 14 and continue: 145 / 21

Let's proceed to step 3:
145 divided by 21 is 6 with a remainder of 19.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 126 from 145 and we're left with 19.
Append the next digit (8) from the dividend to 19 and continue with: 198 / 21

Moving on to step 4:
If we divide 198 by 21, we get 9 and a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 69.0
If we subtract 189 from 198, we get 9.
Append the next digit (2) from the dividend to 9 and continue with: 92 / 21

Advancing to step 5:
If we divide 92 by 21, we get 4 and a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 694.0
Subtract 84 from 92 to get 8.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 21

Step 6:
The number 21 fits into 87 4 times, leaving a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 6944.0
Subtracting 84 from 87 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 7:
21 can be fit into 30 1 times, resulting in a remainder of 9.
The next digit of our result is 1. 
Result so far: 6944.1
Subtracting 21 from 30 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
90 divided by 21 is 4 with a remainder of 6.
The next digit of our result is 4. 
Result so far: 6944.14
If we subtract 84 from 90, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 9:
When dividing 60 by 21, we get 2 with a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 6944.142
Subtracting 42 from 60 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 10:
When dividing 180 by 21, we get 8 with a remainder of 12.
The next digit of our result is 8. 
Result so far: 6944.1428
Subtract 168 from 180 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 11:
The number 21 fits into 120 5 times, leaving a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 6944.14285
If we take 105 away from 120, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 12:
21 goes into 150 7 times with a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 6944.142857
If we take 147 away from 150, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 13:
If we divide 30 by 21, we get 1 and a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 6944.1428571
The remainder is 9 after subtracting 21 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 14:
90 divided by 21 is 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 6944.14285714
Deduct 84 from 90 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final result is 6944.14285714 with a remainder of 6e-09.