We're dividing 114629 by 21 
We want to figure out the number of times 114629 can be divided by 21.

Step 1:
The number 21 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 21

Advancing to step 2:
21 goes into 11 0 times with a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 11, we end up with 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 21

Step 3:
114 divided by 21 is 5 with a remainder of 9.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Deduct 105 from 114 and we're left with 9.
Bring next digit (6) of the dividend behind the 9 and repeat the process: 96 / 21

Step 4:
The number 21 fits into 96 4 times, leaving a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 54.0
Subtracting 84 from 96 leaves us with 12.
Bring next digit (2) of the dividend behind the 12 and repeat the process: 122 / 21

Advancing to step 5:
If we divide 122 by 21, we get 5 and a remainder of 17.
Put 5 as the next digit of the answer. 
Result so far: 545.0
If we take 105 away from 122, we end up with 17.
Append the next digit (9) from the dividend to 17 and continue with: 179 / 21

Step 6:
The number 21 fits into 179 8 times, leaving a remainder of 11.
Use 8 as the next digit of our solution. 
Result so far: 5458.0
Subtract 168 from 179 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 7:
If we divide 110 by 21, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 5458.5
Subtracting 105 from 110 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
21 can be fit into 50 2 times, resulting in a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 5458.52
Deduct 42 from 50 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 9:
If we divide 80 by 21, we get 3 and a remainder of 17.
Put 3 as the next digit of the answer. 
Result so far: 5458.523
The remainder is 17 after subtracting 63 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 10:
If we divide 170 by 21, we get 8 and a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 5458.5238
Subtracting 168 from 170 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 11:
21 goes into 20 0 times with a remainder of 20.
The next digit of our result is 0. 
Result so far: 5458.5238
If we subtract 0 from 20, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 12:
21 can be fit into 200 9 times, resulting in a remainder of 11.
Put 9 as the next digit of the answer. 
Result so far: 5458.523809
If we subtract 189 from 200, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 13:
The number 21 fits into 110 5 times, leaving a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 5458.5238095
Subtracting 105 from 110 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 14:
The number 21 fits into 50 2 times, leaving a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 5458.52380952
Subtracting 42 from 50 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 5458.52380952, and the remainder is 8e-09.