We're dividing 3219412 by 409 
We're looking to find how many times 409 goes into 3219412.

Advancing to step 1:
When dividing 3 by 409, 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.
Include the next digit (2) from the dividend after 3, then repeat: 32 / 409

Going ahead to step 2:
The number 409 fits into 32 0 times, leaving a remainder of 32.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 32 and we're left with 32.
Fetch the next digit (1) from the dividend, attach it to 32 and continue: 321 / 409

Let's proceed to step 3:
The number 409 fits into 321 0 times, leaving a remainder of 321.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 321 leaves us with 321.
Bring next digit (9) of the dividend behind the 321 and repeat the process: 3219 / 409

Advancing to step 4:
When dividing 3219 by 409, we get 7 with a remainder of 356.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
The remainder is 356 after subtracting 2863 from 3219.
Grab the next digit (4) from the dividend, add it to 356, then carry on: 3564 / 409

Advancing to step 5:
409 can be fit into 3564 8 times, resulting in a remainder of 292.
Use 8 as the next digit of our solution. 
Result so far: 78.0
Subtracting 3272 from 3564 leaves us with 292.
Include the next digit (1) from the dividend after 292, then repeat: 2921 / 409

Moving on to step 6:
409 goes into 2921 7 times with a remainder of 58.
Record the quotient 7 as the next digit in the result. 
Result so far: 787.0
The remainder is 58 after subtracting 2863 from 2921.
Take the next digit (2) from the dividend and append it to 58, then repeat: 582 / 409

Going ahead to step 7:
582 divided by 409 is 1 with a remainder of 173.
Write down 1 as next digit of the result. 
Result so far: 7871.0
If we subtract 409 from 582, we get 173.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1730, and continue the process.

Going ahead to step 8:
409 goes into 1730 4 times with a remainder of 94.
Put 4 as the next digit of the answer. 
Result so far: 7871.4
Subtracting 1636 from 1730 leaves us with 94.
Since there are no more digits in the dividend, we add a zero to the remainder making it 940, and continue the process.

Going ahead to step 9:
The number 409 fits into 940 2 times, leaving a remainder of 122.
Put 2 as the next digit of the answer. 
Result so far: 7871.42
Subtracting 818 from 940 leaves us with 122.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1220, and continue the process.

Going ahead to step 10:
409 can be fit into 1220 2 times, resulting in a remainder of 402.
Record the quotient 2 as the next digit in the result. 
Result so far: 7871.422
Deduct 818 from 1220 and we're left with 402.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4020, and continue the process.

Our division results in 7871.422 with a remaining 0.0402.