114421 ÷ 37 
We're looking to find how many times 37 goes into 114421.

Advancing to step 1:
When dividing 1 by 37, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 37

Going ahead to step 2:
37 can be fit into 11 0 times, resulting in a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 11 leaves us with 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 37

On to step 3:
114 divided by 37 is 3 with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
The remainder is 3 after subtracting 111 from 114.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 37

On to step 4:
When dividing 34 by 37, we get 0 with a remainder of 34.
Write down 0 as next digit of the result. 
Result so far: 30.0
The remainder is 34 after subtracting 0 from 34.
Bring next digit (2) of the dividend behind the 34 and repeat the process: 342 / 37

Step 5:
If we divide 342 by 37, we get 9 and a remainder of 9.
Use 9 as the next digit of our solution. 
Result so far: 309.0
Subtract 333 from 342 to get 9.
Include the next digit (1) from the dividend after 9, then repeat: 91 / 37

Let's proceed to step 6:
The number 37 fits into 91 2 times, leaving a remainder of 17.
The next digit of our result is 2. 
Result so far: 3092.0
Subtract 74 from 91 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Step 7:
The number 37 fits into 170 4 times, leaving a remainder of 22.
Use 4 as the next digit of our solution. 
Result so far: 3092.4
Subtracting 148 from 170 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 8:
220 divided by 37 is 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 3092.45
Subtracting 185 from 220 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 9:
37 can be fit into 350 9 times, resulting in a remainder of 17.
Record the quotient 9 as the next digit in the result. 
Result so far: 3092.459
The remainder is 17 after subtracting 333 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 10:
37 can be fit into 170 4 times, resulting in a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 3092.4594
Subtract 148 from 170 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 11:
220 divided by 37 is 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 3092.45945
If we take 185 away from 220, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 12:
37 goes into 350 9 times with a remainder of 17.
The next digit of our result is 9. 
Result so far: 3092.459459
If we take 333 away from 350, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 13:
37 goes into 170 4 times with a remainder of 22.
Use 4 as the next digit of our solution. 
Result so far: 3092.4594594
Deduct 148 from 170 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 14:
When dividing 220 by 37, we get 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 3092.45945945
Subtracting 185 from 220 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Our division results in 3092.45945945 with a remaining 3.5e-08.