Let's divide 262153 by 37
Our goal is to divide 262153 by 37.

Step 1:
When dividing 2 by 37, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 37

On to step 2:
37 can be fit into 26 0 times, resulting in a remainder of 26.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 26 to get 26.
Grab the next digit (2) from the dividend, add it to 26, then carry on: 262 / 37

Let's proceed to step 3:
37 can be fit into 262 7 times, resulting in a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtracting 259 from 262 leaves us with 3.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 37

On to step 4:
The number 37 fits into 31 0 times, leaving a remainder of 31.
The number 0 becomes the next digit in our result. 
Result so far: 70.0
If we subtract 0 from 31, we get 31.
Bring next digit (5) of the dividend behind the 31 and repeat the process: 315 / 37

Step 5:
37 can be fit into 315 8 times, resulting in a remainder of 19.
Use 8 as the next digit of our solution. 
Result so far: 708.0
If we take 296 away from 315, we end up with 19.
Append the next digit (3) from the dividend to 19 and continue with: 193 / 37

Moving on to step 6:
37 goes into 193 5 times with a remainder of 8.
Use 5 as the next digit of our solution. 
Result so far: 7085.0
Deduct 185 from 193 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.

Going ahead to step 7:
80 divided by 37 is 2 with a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 7085.2
Subtract 74 from 80 to 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.

Let's proceed to step 8:
The number 37 fits into 60 1 times, leaving a remainder of 23.
The next digit of our result is 1. 
Result so far: 7085.21
If we take 37 away from 60, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 9:
37 can be fit into 230 6 times, resulting in a remainder of 8.
Use 6 as the next digit of our solution. 
Result so far: 7085.216
The remainder is 8 after subtracting 222 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 10:
The number 37 fits into 80 2 times, leaving a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 7085.2162
Subtracting 74 from 80 leaves us 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.

Moving on to step 11:
37 goes into 60 1 times with a remainder of 23.
Use 1 as the next digit of our solution. 
Result so far: 7085.21621
Subtract 37 from 60 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 12:
37 goes into 230 6 times with a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 7085.216216
The remainder is 8 after subtracting 222 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 13:
The number 37 fits into 80 2 times, leaving a remainder of 6.
The next digit of our result is 2. 
Result so far: 7085.2162162
Subtracting 74 from 80 leaves us 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 14:
37 goes into 60 1 times with a remainder of 23.
Record the quotient 1 as the next digit in the result. 
Result so far: 7085.21621621
Deduct 37 from 60 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

In conclusion, the division gives 7085.21621621 with a balance of 2.3e-08.