We look at the division of 113974 by 21 
We want to figure out the number of times 113974 can be divided by 21.

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
Subtract 0 from 1 to get 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 21

Let's proceed to step 2:
21 can be fit into 11 0 times, resulting in a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 11 to get 11.
Fetch the next digit (3) from the dividend, attach it to 11 and continue: 113 / 21

Advancing to step 3:
21 can be fit into 113 5 times, resulting in a remainder of 8.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtract 105 from 113 to get 8.
Append the next digit (9) from the dividend to 8 and continue with: 89 / 21

On to step 4:
21 can be fit into 89 4 times, resulting in a remainder of 5.
The next digit of our result is 4. 
Result so far: 54.0
If we take 84 away from 89, we end up with 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 21

Moving on to step 5:
The number 21 fits into 57 2 times, leaving a remainder of 15.
The number 2 becomes the next digit in our result. 
Result so far: 542.0
If we subtract 42 from 57, we get 15.
Append the next digit (4) from the dividend to 15 and continue with: 154 / 21

On to step 6:
21 goes into 154 7 times with a remainder of 7.
Use 7 as the next digit of our solution. 
Result so far: 5427.0
Subtract 147 from 154 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
If we divide 70 by 21, we get 3 and a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 5427.3
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 8:
21 goes into 70 3 times with a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 5427.33
Deduct 63 from 70 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The final outcome is 5427.33, with a leftover of 0.007.