Let's divide 585903 by 4
Our goal is to divide 585903 by 4.

On to step 1:
4 can be fit into 5 1 times, resulting in a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 4 from 5, we get 1.
Fetch the next digit (8) from the dividend, attach it to 1 and continue: 18 / 4

On to step 2:
4 goes into 18 4 times with a remainder of 2.
The next digit of our result is 4. 
Result so far: 14.0
Subtracting 16 from 18 leaves us with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 4

On to step 3:
If we divide 25 by 4, we get 6 and a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 146.0
Deduct 24 from 25 and we're left with 1.
Fetch the next digit (9) from the dividend, attach it to 1 and continue: 19 / 4

Advancing to step 4:
4 goes into 19 4 times with a remainder of 3.
Write down 4 as next digit of the result. 
Result so far: 1464.0
Subtracting 16 from 19 leaves us with 3.
Include the next digit (0) from the dividend after 3, then repeat: 30 / 4

On to step 5:
4 can be fit into 30 7 times, resulting in a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 14647.0
Subtracting 28 from 30 leaves us with 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 4

Advancing to step 6:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 146475.0
Subtracting 20 from 23 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
If we divide 30 by 4, we get 7 and a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 146475.7
The remainder is 2 after subtracting 28 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 8:
4 goes into 20 5 times with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 146475.75
Subtract 20 from 20 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 9:
The number 4 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 146475.75
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 10:
4 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 146475.75
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 146475.75, and the remainder is 0.0.