116583 ÷ 37 
We're looking to find how many times 37 goes into 116583.

Going ahead to step 1:
If we divide 1 by 37, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 37

Moving on to step 2:
37 goes into 11 0 times with a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 11 leaves us with 11.
Append the next digit (6) from the dividend to 11 and continue with: 116 / 37

Let's proceed to step 3:
The number 37 fits into 116 3 times, leaving a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we subtract 111 from 116, we get 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 37

Step 4:
37 goes into 55 1 times with a remainder of 18.
The number 1 becomes the next digit in our result. 
Result so far: 31.0
Deduct 37 from 55 and we're left with 18.
Append the next digit (8) from the dividend to 18 and continue with: 188 / 37

Going ahead to step 5:
37 goes into 188 5 times with a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 315.0
Subtracting 185 from 188 leaves us with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 37

On to step 6:
33 divided by 37 is 0 with a remainder of 33.
Put 0 as the next digit of the answer. 
Result so far: 3150.0
Deduct 0 from 33 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 7:
If we divide 330 by 37, we get 8 and a remainder of 34.
Use 8 as the next digit of our solution. 
Result so far: 3150.8
If we subtract 296 from 330, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 8:
If we divide 340 by 37, we get 9 and a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 3150.89
Subtracting 333 from 340 leaves us with 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 9:
When dividing 70 by 37, we get 1 with a remainder of 33.
Put 1 as the next digit of the answer. 
Result so far: 3150.891
Subtracting 37 from 70 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 10:
If we divide 330 by 37, we get 8 and a remainder of 34.
Write down 8 as next digit of the result. 
Result so far: 3150.8918
The remainder is 34 after subtracting 296 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 11:
If we divide 340 by 37, we get 9 and a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 3150.89189
Subtracting 333 from 340 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 12:
37 goes into 70 1 times with a remainder of 33.
Write down 1 as next digit of the result. 
Result so far: 3150.891891
Subtracting 37 from 70 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 13:
330 divided by 37 is 8 with a remainder of 34.
Put 8 as the next digit of the answer. 
Result so far: 3150.8918918
Subtracting 296 from 330 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 14:
When dividing 340 by 37, we get 9 with a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 3150.89189189
The remainder is 7 after subtracting 333 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

In conclusion, the division gives 3150.89189189 with a balance of 7e-09.