742517 ÷ 15 
We're looking to find how many times 15 goes into 742517.

Going ahead to step 1:
When dividing 7 by 15, we get 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Append the next digit (4) from the dividend to 7 and continue with: 74 / 15

On to step 2:
The number 15 fits into 74 4 times, leaving 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 (2) from the dividend, attach it to 14 and continue: 142 / 15

On to step 3:
142 divided by 15 is 9 with a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 49.0
The remainder is 7 after subtracting 135 from 142.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 15

Let's proceed to step 4:
15 can be fit into 75 5 times, resulting in a remainder of 0.
The next digit of our result is 5. 
Result so far: 495.0
If we take 75 away from 75, we end up with 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 15

Going ahead to step 5:
15 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 4950.0
Subtract 0 from 1 to get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 15

Advancing to step 6:
If we divide 17 by 15, we get 1 and a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 49501.0
Subtracting 15 from 17 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.

Let's proceed to step 7:
The number 15 fits into 20 1 times, leaving a remainder of 5.
The next digit of our result is 1. 
Result so far: 49501.1
Deduct 15 from 20 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
15 can be fit into 50 3 times, resulting in a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 49501.13
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 9:
15 can be fit into 50 3 times, resulting in a remainder of 5.
The next digit of our result is 3. 
Result so far: 49501.133
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

After the division, we end up with 49501.133 and a remainder of 0.0005.