321257 ÷ 45 
Our goal is to divide 321257 by 45.

On to step 1:
45 can be fit into 3 0 times, resulting in a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 45

Let's proceed to step 2:
If we divide 32 by 45, we get 0 and a remainder of 32.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 32, we end up with 32.
Grab the next digit (1) from the dividend, add it to 32, then carry on: 321 / 45

On to step 3:
When dividing 321 by 45, we get 7 with a remainder of 6.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
The remainder is 6 after subtracting 315 from 321.
Append the next digit (2) from the dividend to 6 and continue with: 62 / 45

Let's proceed to step 4:
If we divide 62 by 45, we get 1 and a remainder of 17.
Put 1 as the next digit of the answer. 
Result so far: 71.0
Subtract 45 from 62 to get 17.
Append the next digit (5) from the dividend to 17 and continue with: 175 / 45

On to step 5:
45 can be fit into 175 3 times, resulting in a remainder of 40.
Write down 3 as next digit of the result. 
Result so far: 713.0
Subtract 135 from 175 to get 40.
Bring next digit (7) of the dividend behind the 40 and repeat the process: 407 / 45

Moving on to step 6:
407 divided by 45 is 9 with a remainder of 2.
The next digit of our result is 9. 
Result so far: 7139.0
Subtracting 405 from 407 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 7:
45 can be fit into 20 0 times, resulting in a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 7139.0
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
200 divided by 45 is 4 with a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 7139.04
Deduct 180 from 200 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.

Moving on to step 9:
If we divide 200 by 45, we get 4 and a remainder of 20.
Write down 4 as next digit of the result. 
Result so far: 7139.044
Deduct 180 from 200 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.

In conclusion, the division gives 7139.044 with a balance of 0.002.