Let's divide 106594 by 3
We're looking to find how many times 3 goes into 106594.

Step 1:
If we divide 1 by 3, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 3

Advancing to step 2:
3 can be fit into 10 3 times, resulting in a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 9 from 10, we get 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 3

Step 3:
The number 3 fits into 16 5 times, leaving a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 35.0
Subtract 15 from 16 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Moving on to step 4:
If we divide 15 by 3, we get 5 and a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 355.0
If we take 15 away from 15, we end up with 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 3

Going ahead to step 5:
3 can be fit into 9 3 times, resulting in a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 3553.0
Subtracting 9 from 9 leaves us with 0.
Include the next digit (4) from the dividend after 0, then repeat: 4 / 3

Going ahead to step 6:
When dividing 4 by 3, we get 1 with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 35531.0
The remainder is 1 after subtracting 3 from 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
3 goes into 10 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 35531.3
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 8:
The number 3 fits into 10 3 times, leaving a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 35531.33
Deduct 9 from 10 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.

The quotient of the division is 35531.33, and the remainder is 0.001.