We look at the division of 645172 by 15 
Our goal is to divide 645172 by 15.

Step 1:
15 can be fit into 6 0 times, resulting in a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 15

Going ahead to step 2:
When dividing 64 by 15, we get 4 with a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Subtracting 60 from 64 leaves us with 4.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 15

Let's proceed to step 3:
The number 15 fits into 45 3 times, leaving a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 43.0
Deduct 45 from 45 and we're left with 0.
Fetch the next digit (1) from the dividend, attach it to 0 and continue: 1 / 15

Advancing to step 4:
15 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 430.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 15

On to step 5:
When dividing 17 by 15, we get 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 4301.0
Subtracting 15 from 17 leaves us with 2.
Grab the next digit (2) from the dividend, add it to 2, then carry on: 22 / 15

Moving on to step 6:
The number 15 fits into 22 1 times, leaving a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 43011.0
The remainder is 7 after subtracting 15 from 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
15 can be fit into 70 4 times, resulting in a remainder of 10.
The next digit of our result is 4. 
Result so far: 43011.4
Subtracting 60 from 70 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.

On to step 8:
100 divided by 15 is 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 43011.46
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.

Step 9:
When dividing 100 by 15, we get 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 43011.466
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.

The quotient of the division is 43011.466, and the remainder is 0.001.