We're dividing 370336 by 34 
We're looking to find how many times 34 goes into 370336.

Step 1:
The number 34 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 34

Moving on to step 2:
The number 34 fits into 37 1 times, leaving a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 34 from 37 and we're left with 3.
Include the next digit (0) from the dividend after 3, then repeat: 30 / 34

Moving on to step 3:
When dividing 30 by 34, we get 0 with a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 10.0
Subtract 0 from 30 to get 30.
Grab the next digit (3) from the dividend, add it to 30, then carry on: 303 / 34

Moving on to step 4:
34 goes into 303 8 times with a remainder of 31.
Record the quotient 8 as the next digit in the result. 
Result so far: 108.0
Deduct 272 from 303 and we're left with 31.
Fetch the next digit (3) from the dividend, attach it to 31 and continue: 313 / 34

Moving on to step 5:
The number 34 fits into 313 9 times, leaving a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 1089.0
Subtracting 306 from 313 leaves us with 7.
Fetch the next digit (6) from the dividend, attach it to 7 and continue: 76 / 34

Advancing to step 6:
34 can be fit into 76 2 times, resulting in a remainder of 8.
The next digit of our result is 2. 
Result so far: 10892.0
Deduct 68 from 76 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 7:
34 can be fit into 80 2 times, resulting in a remainder of 12.
The next digit of our result is 2. 
Result so far: 10892.2
Subtract 68 from 80 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 8:
The number 34 fits into 120 3 times, leaving a remainder of 18.
Put 3 as the next digit of the answer. 
Result so far: 10892.23
Subtracting 102 from 120 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 9:
34 goes into 180 5 times with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 10892.235
The remainder is 10 after subtracting 170 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
34 goes into 100 2 times with a remainder of 32.
Use 2 as the next digit of our solution. 
Result so far: 10892.2352
The remainder is 32 after subtracting 68 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 11:
34 can be fit into 320 9 times, resulting in a remainder of 14.
Use 9 as the next digit of our solution. 
Result so far: 10892.23529
The remainder is 14 after subtracting 306 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 12:
If we divide 140 by 34, we get 4 and a remainder of 4.
The next digit of our result is 4. 
Result so far: 10892.235294
Subtract 136 from 140 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 13:
34 can be fit into 40 1 times, resulting in a remainder of 6.
The next digit of our result is 1. 
Result so far: 10892.2352941
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.

On to step 14:
The number 34 fits into 60 1 times, leaving a remainder of 26.
The next digit of our result is 1. 
Result so far: 10892.23529411
Deduct 34 from 60 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

After the division, we end up with 10892.23529411 and a remainder of 2.6e-08.