We're dividing 373596 by 34 
We want to figure out the number of times 373596 can be divided by 34.

Moving on to step 1:
34 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 34

On to step 2:
When dividing 37 by 34, we get 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 34 from 37 and we're left with 3.
Grab the next digit (3) from the dividend, add it to 3, then carry on: 33 / 34

Moving on to step 3:
When dividing 33 by 34, we get 0 with a remainder of 33.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we subtract 0 from 33, we get 33.
Grab the next digit (5) from the dividend, add it to 33, then carry on: 335 / 34

Advancing to step 4:
The number 34 fits into 335 9 times, leaving a remainder of 29.
Record the quotient 9 as the next digit in the result. 
Result so far: 109.0
Deduct 306 from 335 and we're left with 29.
Take the next digit (9) from the dividend and append it to 29, then repeat: 299 / 34

On to step 5:
34 goes into 299 8 times with a remainder of 27.
The number 8 becomes the next digit in our result. 
Result so far: 1098.0
The remainder is 27 after subtracting 272 from 299.
Append the next digit (6) from the dividend to 27 and continue with: 276 / 34

Step 6:
34 can be fit into 276 8 times, resulting in a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 10988.0
The remainder is 4 after subtracting 272 from 276.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
When dividing 40 by 34, we get 1 with a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 10988.1
If we take 34 away from 40, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 8:
34 can be fit into 60 1 times, resulting in a remainder of 26.
Use 1 as the next digit of our solution. 
Result so far: 10988.11
The remainder is 26 after subtracting 34 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The quotient of the division is 10988.11, and the remainder is 0.026.