We're dividing 743569 by 15 
We're looking to find how many times 15 goes into 743569.

Advancing to step 1:
7 divided by 15 is 0 with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Take the next digit (4) from the dividend and append it to 7, then repeat: 74 / 15

Going ahead to step 2:
74 divided by 15 is 4 with a remainder of 14.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
If we subtract 60 from 74, we get 14.
Fetch the next digit (3) from the dividend, attach it to 14 and continue: 143 / 15

On to step 3:
If we divide 143 by 15, we get 9 and a remainder of 8.
The next digit of our result is 9. 
Result so far: 49.0
If we take 135 away from 143, we end up with 8.
Fetch the next digit (5) from the dividend, attach it to 8 and continue: 85 / 15

On to step 4:
When dividing 85 by 15, we get 5 with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 495.0
The remainder is 10 after subtracting 75 from 85.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 15

Moving on to step 5:
The number 15 fits into 106 7 times, leaving a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 4957.0
If we subtract 105 from 106, we get 1.
Take the next digit (9) from the dividend and append it to 1, then repeat: 19 / 15

Moving on to step 6:
The number 15 fits into 19 1 times, leaving a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 49571.0
Subtract 15 from 19 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
40 divided by 15 is 2 with a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 49571.2
Subtracting 30 from 40 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
If we divide 100 by 15, we get 6 and a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 49571.26
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 9:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 49571.266
If we take 90 away from 100, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The final result is 49571.266 with a remainder of 0.001.