Let's divide 637381 by 113
We want to figure out the number of times 637381 can be divided by 113.

Step 1:
The number 113 fits into 6 0 times, leaving a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (3) from the dividend after 6, then repeat: 63 / 113

Let's proceed to step 2:
113 goes into 63 0 times with a remainder of 63.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 63 to get 63.
Grab the next digit (7) from the dividend, add it to 63, then carry on: 637 / 113

Going ahead to step 3:
When dividing 637 by 113, we get 5 with a remainder of 72.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we take 565 away from 637, we end up with 72.
Bring next digit (3) of the dividend behind the 72 and repeat the process: 723 / 113

Going ahead to step 4:
If we divide 723 by 113, we get 6 and a remainder of 45.
The next digit of our result is 6. 
Result so far: 56.0
If we subtract 678 from 723, we get 45.
Include the next digit (8) from the dividend after 45, then repeat: 458 / 113

On to step 5:
When dividing 458 by 113, we get 4 with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 564.0
The remainder is 6 after subtracting 452 from 458.
Grab the next digit (1) from the dividend, add it to 6, then carry on: 61 / 113

Moving on to step 6:
The number 113 fits into 61 0 times, leaving a remainder of 61.
Write down 0 as next digit of the result. 
Result so far: 5640.0
The remainder is 61 after subtracting 0 from 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

On to step 7:
113 goes into 610 5 times with a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 5640.5
The remainder is 45 after subtracting 565 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

On to step 8:
113 can be fit into 450 3 times, resulting in a remainder of 111.
The next digit of our result is 3. 
Result so far: 5640.53
Subtracting 339 from 450 leaves us with 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1110, and continue the process.

On to step 9:
113 goes into 1110 9 times with a remainder of 93.
Put 9 as the next digit of the answer. 
Result so far: 5640.539
If we take 1017 away from 1110, we end up with 93.
Since there are no more digits in the dividend, we add a zero to the remainder making it 930, and continue the process.

Step 10:
930 divided by 113 is 8 with a remainder of 26.
The number 8 becomes the next digit in our result. 
Result so far: 5640.5398
Deduct 904 from 930 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 11:
113 can be fit into 260 2 times, resulting in a remainder of 34.
Use 2 as the next digit of our solution. 
Result so far: 5640.53982
Subtracting 226 from 260 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 12:
The number 113 fits into 340 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 5640.539823
If we subtract 339 from 340, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 13:
When dividing 10 by 113, we get 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 5640.539823
If we take 0 away from 10, we end up 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 14:
100 divided by 113 is 0 with a remainder of 100.
Put 0 as the next digit of the answer. 
Result so far: 5640.539823
Deduct 0 from 100 and we're left with 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1000, and continue the process.

In conclusion, the division gives 5640.539823 with a balance of 1e-07.