We're dividing 15338374 by 584 
Let's see how many times 584 fits into 15338374.

Step 1:
1 divided by 584 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 584

Moving on to step 2:
When dividing 15 by 584, we get 0 with a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Fetch the next digit (3) from the dividend, attach it to 15 and continue: 153 / 584

On to step 3:
584 can be fit into 153 0 times, resulting in a remainder of 153.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 153, we get 153.
Fetch the next digit (3) from the dividend, attach it to 153 and continue: 1533 / 584

On to step 4:
If we divide 1533 by 584, we get 2 and a remainder of 365.
Use 2 as the next digit of our solution. 
Result so far: 2.0
The remainder is 365 after subtracting 1168 from 1533.
Include the next digit (8) from the dividend after 365, then repeat: 3658 / 584

Step 5:
584 goes into 3658 6 times with a remainder of 154.
Use 6 as the next digit of our solution. 
Result so far: 26.0
Subtract 3504 from 3658 to get 154.
Include the next digit (3) from the dividend after 154, then repeat: 1543 / 584

Moving on to step 6:
The number 584 fits into 1543 2 times, leaving a remainder of 375.
Use 2 as the next digit of our solution. 
Result so far: 262.0
Subtracting 1168 from 1543 leaves us with 375.
Take the next digit (7) from the dividend and append it to 375, then repeat: 3757 / 584

Moving on to step 7:
584 can be fit into 3757 6 times, resulting in a remainder of 253.
Put 6 as the next digit of the answer. 
Result so far: 2626.0
If we subtract 3504 from 3757, we get 253.
Append the next digit (4) from the dividend to 253 and continue with: 2534 / 584

Step 8:
584 goes into 2534 4 times with a remainder of 198.
Use 4 as the next digit of our solution. 
Result so far: 26264.0
Subtract 2336 from 2534 to get 198.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1980, and continue the process.

Let's proceed to step 9:
If we divide 1980 by 584, we get 3 and a remainder of 228.
The next digit of our result is 3. 
Result so far: 26264.3
Deduct 1752 from 1980 and we're left with 228.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2280, and continue the process.

Moving on to step 10:
When dividing 2280 by 584, we get 3 with a remainder of 528.
The number 3 becomes the next digit in our result. 
Result so far: 26264.33
The remainder is 528 after subtracting 1752 from 2280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5280, and continue the process.

The quotient of the division is 26264.33, and the remainder is 0.528.