We're dividing 319343 by 361 
We're looking to find how many times 361 goes into 319343.

Advancing to step 1:
When dividing 3 by 361, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 361

Step 2:
When dividing 31 by 361, we get 0 with a remainder of 31.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 31 and we're left with 31.
Include the next digit (9) from the dividend after 31, then repeat: 319 / 361

Going ahead to step 3:
The number 361 fits into 319 0 times, leaving a remainder of 319.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 319 to get 319.
Include the next digit (3) from the dividend after 319, then repeat: 3193 / 361

Moving on to step 4:
The number 361 fits into 3193 8 times, leaving a remainder of 305.
Put 8 as the next digit of the answer. 
Result so far: 8.0
If we subtract 2888 from 3193, we get 305.
Include the next digit (4) from the dividend after 305, then repeat: 3054 / 361

On to step 5:
361 can be fit into 3054 8 times, resulting in a remainder of 166.
Record the quotient 8 as the next digit in the result. 
Result so far: 88.0
If we subtract 2888 from 3054, we get 166.
Bring next digit (3) of the dividend behind the 166 and repeat the process: 1663 / 361

Step 6:
The number 361 fits into 1663 4 times, leaving a remainder of 219.
The number 4 becomes the next digit in our result. 
Result so far: 884.0
The remainder is 219 after subtracting 1444 from 1663.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2190, and continue the process.

Let's proceed to step 7:
2190 divided by 361 is 6 with a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 884.6
Subtracting 2166 from 2190 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 8:
361 goes into 240 0 times with a remainder of 240.
Use 0 as the next digit of our solution. 
Result so far: 884.6
Subtract 0 from 240 to get 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2400, and continue the process.

Moving on to step 9:
When dividing 2400 by 361, we get 6 with a remainder of 234.
The number 6 becomes the next digit in our result. 
Result so far: 884.606
Deduct 2166 from 2400 and we're left with 234.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2340, and continue the process.

Advancing to step 10:
If we divide 2340 by 361, we get 6 and a remainder of 174.
Use 6 as the next digit of our solution. 
Result so far: 884.6066
If we take 2166 away from 2340, we end up with 174.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1740, and continue the process.

The quotient of the division is 884.6066, and the remainder is 0.00174.