We look at the division of 319364 by 45 
We're looking to find how many times 45 goes into 319364.

Step 1:
45 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 45

Moving on to step 2:
45 can be fit into 31 0 times, resulting in a remainder of 31.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 31 leaves us with 31.
Append the next digit (9) from the dividend to 31 and continue with: 319 / 45

Let's proceed to step 3:
45 can be fit into 319 7 times, resulting in a remainder of 4.
Write down 7 as next digit of the result. 
Result so far: 7.0
If we subtract 315 from 319, we get 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 45

Let's proceed to step 4:
45 can be fit into 43 0 times, resulting in a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 70.0
The remainder is 43 after subtracting 0 from 43.
Grab the next digit (6) from the dividend, add it to 43, then carry on: 436 / 45

Let's proceed to step 5:
436 divided by 45 is 9 with a remainder of 31.
The number 9 becomes the next digit in our result. 
Result so far: 709.0
Subtract 405 from 436 to get 31.
Take the next digit (4) from the dividend and append it to 31, then repeat: 314 / 45

Moving on to step 6:
If we divide 314 by 45, we get 6 and a remainder of 44.
Use 6 as the next digit of our solution. 
Result so far: 7096.0
Deduct 270 from 314 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 7:
If we divide 440 by 45, we get 9 and a remainder of 35.
The next digit of our result is 9. 
Result so far: 7096.9
The remainder is 35 after subtracting 405 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 8:
When dividing 350 by 45, we get 7 with a remainder of 35.
Record the quotient 7 as the next digit in the result. 
Result so far: 7096.97
Subtracting 315 from 350 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 9:
350 divided by 45 is 7 with a remainder of 35.
Record the quotient 7 as the next digit in the result. 
Result so far: 7096.977
The remainder is 35 after subtracting 315 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The final result is 7096.977 with a remainder of 0.0035.