We look at the division of 969541 by 15 
We're looking to find how many times 15 goes into 969541.

Let's proceed to step 1:
9 divided by 15 is 0 with a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Take the next digit (6) from the dividend and append it to 9, then repeat: 96 / 15

Advancing to step 2:
96 divided by 15 is 6 with a remainder of 6.
The next digit of our result is 6. 
Result so far: 6.0
If we subtract 90 from 96, we get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 15

Let's proceed to step 3:
15 can be fit into 69 4 times, resulting in a remainder of 9.
Put 4 as the next digit of the answer. 
Result so far: 64.0
Subtract 60 from 69 to get 9.
Bring next digit (5) of the dividend behind the 9 and repeat the process: 95 / 15

Going ahead to step 4:
15 can be fit into 95 6 times, resulting in a remainder of 5.
The next digit of our result is 6. 
Result so far: 646.0
Subtracting 90 from 95 leaves us with 5.
Grab the next digit (4) from the dividend, add it to 5, then carry on: 54 / 15

On to step 5:
The number 15 fits into 54 3 times, leaving a remainder of 9.
Use 3 as the next digit of our solution. 
Result so far: 6463.0
The remainder is 9 after subtracting 45 from 54.
Append the next digit (1) from the dividend to 9 and continue with: 91 / 15

On to step 6:
When dividing 91 by 15, we get 6 with a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 64636.0
Deduct 90 from 91 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
10 divided by 15 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 64636.0
Subtracting 0 from 10 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.

Step 8:
15 goes into 100 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 64636.06
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.

Step 9:
The number 15 fits into 100 6 times, leaving a remainder of 10.
The next digit of our result is 6. 
Result so far: 64636.066
Subtracting 90 from 100 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.

The final outcome is 64636.066, with a leftover of 0.001.