345561 ÷ 80 
Our goal is to divide 345561 by 80.

Advancing to step 1:
The number 80 fits into 3 0 times, leaving a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 80

Moving on to step 2:
The number 80 fits into 34 0 times, leaving a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 34, we end up with 34.
Take the next digit (5) from the dividend and append it to 34, then repeat: 345 / 80

Moving on to step 3:
80 can be fit into 345 4 times, resulting in a remainder of 25.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we subtract 320 from 345, we get 25.
Grab the next digit (5) from the dividend, add it to 25, then carry on: 255 / 80

Going ahead to step 4:
80 goes into 255 3 times with a remainder of 15.
Record the quotient 3 as the next digit in the result. 
Result so far: 43.0
Deduct 240 from 255 and we're left with 15.
Include the next digit (6) from the dividend after 15, then repeat: 156 / 80

On to step 5:
80 goes into 156 1 times with a remainder of 76.
The next digit of our result is 1. 
Result so far: 431.0
Subtract 80 from 156 to get 76.
Fetch the next digit (1) from the dividend, attach it to 76 and continue: 761 / 80

Moving on to step 6:
When dividing 761 by 80, we get 9 with a remainder of 41.
Use 9 as the next digit of our solution. 
Result so far: 4319.0
Deduct 720 from 761 and we're left with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Advancing to step 7:
410 divided by 80 is 5 with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 4319.5
The remainder is 10 after subtracting 400 from 410.
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 8:
The number 80 fits into 100 1 times, leaving a remainder of 20.
Put 1 as the next digit of the answer. 
Result so far: 4319.51
Deduct 80 from 100 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
80 goes into 200 2 times with a remainder of 40.
The number 2 becomes the next digit in our result. 
Result so far: 4319.512
Subtracting 160 from 200 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 10:
80 can be fit into 400 5 times, resulting in a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 4319.5125
Subtracting 400 from 400 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 11:
If we divide 0 by 80, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 4319.5125
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 12:
0 divided by 80 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 4319.5125
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 4319.5125, and the remainder is 0.0.