We look at the division of 8372588 by 721 
Our goal is to divide 8372588 by 721.

Let's proceed to step 1:
721 goes into 8 0 times with a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Take the next digit (3) from the dividend and append it to 8, then repeat: 83 / 721

Moving on to step 2:
83 divided by 721 is 0 with a remainder of 83.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 83, we get 83.
Include the next digit (7) from the dividend after 83, then repeat: 837 / 721

Step 3:
If we divide 837 by 721, we get 1 and a remainder of 116.
The next digit of our result is 1. 
Result so far: 1.0
If we take 721 away from 837, we end up with 116.
Take the next digit (2) from the dividend and append it to 116, then repeat: 1162 / 721

Step 4:
721 goes into 1162 1 times with a remainder of 441.
Put 1 as the next digit of the answer. 
Result so far: 11.0
Subtracting 721 from 1162 leaves us with 441.
Append the next digit (5) from the dividend to 441 and continue with: 4415 / 721

Moving on to step 5:
721 goes into 4415 6 times with a remainder of 89.
The number 6 becomes the next digit in our result. 
Result so far: 116.0
If we subtract 4326 from 4415, we get 89.
Fetch the next digit (8) from the dividend, attach it to 89 and continue: 898 / 721

Advancing to step 6:
721 goes into 898 1 times with a remainder of 177.
The number 1 becomes the next digit in our result. 
Result so far: 1161.0
If we subtract 721 from 898, we get 177.
Take the next digit (8) from the dividend and append it to 177, then repeat: 1778 / 721

On to step 7:
When dividing 1778 by 721, we get 2 with a remainder of 336.
Put 2 as the next digit of the answer. 
Result so far: 11612.0
If we take 1442 away from 1778, we end up with 336.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3360, and continue the process.

Going ahead to step 8:
721 goes into 3360 4 times with a remainder of 476.
Write down 4 as next digit of the result. 
Result so far: 11612.4
If we subtract 2884 from 3360, we get 476.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4760, and continue the process.

Going ahead to step 9:
When dividing 4760 by 721, we get 6 with a remainder of 434.
The number 6 becomes the next digit in our result. 
Result so far: 11612.46
Deduct 4326 from 4760 and we're left with 434.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4340, and continue the process.

Advancing to step 10:
721 can be fit into 4340 6 times, resulting in a remainder of 14.
Record the quotient 6 as the next digit in the result. 
Result so far: 11612.466
Subtract 4326 from 4340 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The final outcome is 11612.466, with a leftover of 0.0014.