Let's divide 321409 by 45
Let's see how many times 45 fits into 321409.

On to step 1:
If we divide 3 by 45, we get 0 and a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (2) from the dividend to 3 and continue with: 32 / 45

Moving on to step 2:
If we divide 32 by 45, we get 0 and a remainder of 32.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 32, we get 32.
Take the next digit (1) from the dividend and append it to 32, then repeat: 321 / 45

Moving on to step 3:
The number 45 fits into 321 7 times, leaving a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 7.0
Subtracting 315 from 321 leaves us with 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 45

On to step 4:
When dividing 64 by 45, we get 1 with a remainder of 19.
The next digit of our result is 1. 
Result so far: 71.0
Deduct 45 from 64 and we're left with 19.
Bring next digit (0) of the dividend behind the 19 and repeat the process: 190 / 45

Going ahead to step 5:
The number 45 fits into 190 4 times, leaving a remainder of 10.
The next digit of our result is 4. 
Result so far: 714.0
Subtracting 180 from 190 leaves us with 10.
Bring next digit (9) of the dividend behind the 10 and repeat the process: 109 / 45

Advancing to step 6:
45 can be fit into 109 2 times, resulting in a remainder of 19.
Use 2 as the next digit of our solution. 
Result so far: 7142.0
Subtracting 90 from 109 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
If we divide 190 by 45, we get 4 and a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 7142.4
Deduct 180 from 190 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 8:
45 can be fit into 100 2 times, resulting in a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 7142.42
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 9:
45 goes into 100 2 times with a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 7142.422
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.

The quotient of the division is 7142.422, and the remainder is 0.001.