We're dividing 101629 by 15 
We want to figure out the number of times 101629 can be divided by 15.

Step 1:
15 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 15

Moving on to step 2:
When dividing 10 by 15, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Include the next digit (1) from the dividend after 10, then repeat: 101 / 15

Going ahead to step 3:
101 divided by 15 is 6 with a remainder of 11.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 11 after subtracting 90 from 101.
Bring next digit (6) of the dividend behind the 11 and repeat the process: 116 / 15

On to step 4:
116 divided by 15 is 7 with a remainder of 11.
Put 7 as the next digit of the answer. 
Result so far: 67.0
Deduct 105 from 116 and we're left with 11.
Include the next digit (2) from the dividend after 11, then repeat: 112 / 15

Step 5:
When dividing 112 by 15, we get 7 with a remainder of 7.
Write down 7 as next digit of the result. 
Result so far: 677.0
Deduct 105 from 112 and we're left with 7.
Include the next digit (9) from the dividend after 7, then repeat: 79 / 15

Let's proceed to step 6:
The number 15 fits into 79 5 times, leaving a remainder of 4.
The next digit of our result is 5. 
Result so far: 6775.0
Subtract 75 from 79 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.

Moving on to step 7:
15 can be fit into 40 2 times, resulting in a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 6775.2
Deduct 30 from 40 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.

Advancing to step 8:
If we divide 100 by 15, we get 6 and a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 6775.26
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.

On to step 9:
15 can be fit into 100 6 times, resulting in a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 6775.266
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 6775.266 and a remainder of 0.001.