We're dividing 370953 by 13 
We're looking to find how many times 13 goes into 370953.

Step 1:
13 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 13

Moving on to step 2:
If we divide 37 by 13, we get 2 and a remainder of 11.
Put 2 as the next digit of the answer. 
Result so far: 2.0
The remainder is 11 after subtracting 26 from 37.
Include the next digit (0) from the dividend after 11, then repeat: 110 / 13

Let's proceed to step 3:
If we divide 110 by 13, we get 8 and a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 28.0
If we subtract 104 from 110, we get 6.
Append the next digit (9) from the dividend to 6 and continue with: 69 / 13

Advancing to step 4:
The number 13 fits into 69 5 times, leaving a remainder of 4.
The next digit of our result is 5. 
Result so far: 285.0
Subtract 65 from 69 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 13

On to step 5:
45 divided by 13 is 3 with a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 2853.0
Deduct 39 from 45 and we're left with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 13

On to step 6:
13 goes into 63 4 times with a remainder of 11.
Put 4 as the next digit of the answer. 
Result so far: 28534.0
The remainder is 11 after subtracting 52 from 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 7:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 28534.8
If we take 104 away from 110, 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 8:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 28534.84
If we take 52 away from 60, we end up 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.

Advancing to step 9:
If we divide 80 by 13, we get 6 and a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 28534.846
If we take 78 away from 80, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 10:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The next digit of our result is 1. 
Result so far: 28534.8461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 11:
13 can be fit into 70 5 times, resulting in a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 28534.84615
Deduct 65 from 70 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 12:
If we divide 50 by 13, we get 3 and a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 28534.846153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 13:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 28534.8461538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 14:
13 goes into 60 4 times with a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 28534.84615384
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

In conclusion, the division gives 28534.84615384 with a balance of 8e-09.