We look at the division of 580363 by 37 
We're looking to find how many times 37 goes into 580363.

Step 1:
The number 37 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 37

Going ahead to step 2:
37 goes into 58 1 times with a remainder of 21.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 37 from 58 leaves us with 21.
Include the next digit (0) from the dividend after 21, then repeat: 210 / 37

Advancing to step 3:
37 can be fit into 210 5 times, resulting in a remainder of 25.
The next digit of our result is 5. 
Result so far: 15.0
If we take 185 away from 210, we end up with 25.
Include the next digit (3) from the dividend after 25, then repeat: 253 / 37

Step 4:
253 divided by 37 is 6 with a remainder of 31.
The number 6 becomes the next digit in our result. 
Result so far: 156.0
Deduct 222 from 253 and we're left with 31.
Grab the next digit (6) from the dividend, add it to 31, then carry on: 316 / 37

Moving on to step 5:
If we divide 316 by 37, we get 8 and a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 1568.0
Subtract 296 from 316 to get 20.
Include the next digit (3) from the dividend after 20, then repeat: 203 / 37

Let's proceed to step 6:
If we divide 203 by 37, we get 5 and a remainder of 18.
The number 5 becomes the next digit in our result. 
Result so far: 15685.0
Subtract 185 from 203 to get 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 7:
37 goes into 180 4 times with a remainder of 32.
Put 4 as the next digit of the answer. 
Result so far: 15685.4
Subtracting 148 from 180 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 8:
37 goes into 320 8 times with a remainder of 24.
Put 8 as the next digit of the answer. 
Result so far: 15685.48
If we subtract 296 from 320, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 9:
240 divided by 37 is 6 with a remainder of 18.
The number 6 becomes the next digit in our result. 
Result so far: 15685.486
Subtract 222 from 240 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 10:
37 can be fit into 180 4 times, resulting in a remainder of 32.
Write down 4 as next digit of the result. 
Result so far: 15685.4864
The remainder is 32 after subtracting 148 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 11:
37 goes into 320 8 times with a remainder of 24.
Put 8 as the next digit of the answer. 
Result so far: 15685.48648
If we subtract 296 from 320, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 12:
240 divided by 37 is 6 with a remainder of 18.
Write down 6 as next digit of the result. 
Result so far: 15685.486486
Deduct 222 from 240 and we're left 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.

Moving on to step 13:
180 divided by 37 is 4 with a remainder of 32.
Use 4 as the next digit of our solution. 
Result so far: 15685.4864864
The remainder is 32 after subtracting 148 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 14:
When dividing 320 by 37, we get 8 with a remainder of 24.
Use 8 as the next digit of our solution. 
Result so far: 15685.48648648
Subtract 296 from 320 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Our division results in 15685.48648648 with a remaining 2.4e-08.