We look at the division of 319576 by 45 
We want to divide 319576 by 45.

Advancing to step 1:
The number 45 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 45

Advancing to step 2:
When dividing 31 by 45, we get 0 with a remainder of 31.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 31, we get 31.
Include the next digit (9) from the dividend after 31, then repeat: 319 / 45

Moving on to step 3:
If we divide 319 by 45, we get 7 and a remainder of 4.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtracting 315 from 319 leaves us with 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 45

On to step 4:
When dividing 45 by 45, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 71.0
If we subtract 45 from 45, we get 0.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 45

Advancing to step 5:
The number 45 fits into 7 0 times, leaving a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 710.0
Deduct 0 from 7 and we're left with 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 45

Going ahead to step 6:
76 divided by 45 is 1 with a remainder of 31.
The number 1 becomes the next digit in our result. 
Result so far: 7101.0
Subtracting 45 from 76 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 7:
If we divide 310 by 45, we get 6 and a remainder of 40.
Use 6 as the next digit of our solution. 
Result so far: 7101.6
Deduct 270 from 310 and we're left 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.

Going ahead to step 8:
45 goes into 400 8 times with a remainder of 40.
Record the quotient 8 as the next digit in the result. 
Result so far: 7101.68
If we subtract 360 from 400, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 9:
When dividing 400 by 45, we get 8 with a remainder of 40.
The next digit of our result is 8. 
Result so far: 7101.688
If we subtract 360 from 400, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The quotient of the division is 7101.688, and the remainder is 0.004.