We're dividing 343596 by 45 
We want to figure out the number of times 343596 can be divided by 45.

Let's proceed to step 1:
When dividing 3 by 45, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 45

Moving on to step 2:
45 can be fit into 34 0 times, resulting in a remainder of 34.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 34 leaves us with 34.
Grab the next digit (3) from the dividend, add it to 34, then carry on: 343 / 45

Advancing to step 3:
45 can be fit into 343 7 times, resulting in a remainder of 28.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtracting 315 from 343 leaves us with 28.
Grab the next digit (5) from the dividend, add it to 28, then carry on: 285 / 45

Step 4:
If we divide 285 by 45, we get 6 and a remainder of 15.
Use 6 as the next digit of our solution. 
Result so far: 76.0
Deduct 270 from 285 and we're left with 15.
Append the next digit (9) from the dividend to 15 and continue with: 159 / 45

Step 5:
45 can be fit into 159 3 times, resulting in a remainder of 24.
Write down 3 as next digit of the result. 
Result so far: 763.0
Subtract 135 from 159 to get 24.
Include the next digit (6) from the dividend after 24, then repeat: 246 / 45

Going ahead to step 6:
If we divide 246 by 45, we get 5 and a remainder of 21.
The number 5 becomes the next digit in our result. 
Result so far: 7635.0
Deduct 225 from 246 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
When dividing 210 by 45, we get 4 with a remainder of 30.
Use 4 as the next digit of our solution. 
Result so far: 7635.4
The remainder is 30 after subtracting 180 from 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
45 goes into 300 6 times with a remainder of 30.
Use 6 as the next digit of our solution. 
Result so far: 7635.46
Subtract 270 from 300 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 9:
If we divide 300 by 45, we get 6 and a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 7635.466
If we take 270 away from 300, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 7635.466, and the remainder is 0.003.