We look at the division of 583376 by 6 
We're looking to find how many times 6 goes into 583376.

Let's proceed to step 1:
6 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 6

Going ahead to step 2:
When dividing 58 by 6, we get 9 with a remainder of 4.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Subtract 54 from 58 to get 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 6

Moving on to step 3:
If we divide 43 by 6, we get 7 and a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 97.0
Subtracting 42 from 43 leaves us with 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 6

Step 4:
The number 6 fits into 13 2 times, leaving a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 972.0
Subtract 12 from 13 to get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 6

Going ahead to step 5:
6 can be fit into 17 2 times, resulting in a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 9722.0
Subtracting 12 from 17 leaves us with 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Going ahead to step 6:
When dividing 56 by 6, we get 9 with a remainder of 2.
Use 9 as the next digit of our solution. 
Result so far: 97229.0
Subtract 54 from 56 to get 2.
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 7:
When dividing 20 by 6, we get 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 97229.3
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 97229.33
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Our division results in 97229.33 with a remaining 0.002.