95565 ÷ 37 
Our goal is to divide 95565 by 37.

Going ahead to step 1:
The number 37 fits into 9 0 times, leaving a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 9, we end up with 9.
Bring next digit (5) of the dividend behind the 9 and repeat the process: 95 / 37

On to step 2:
37 goes into 95 2 times with a remainder of 21.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtract 74 from 95 to get 21.
Append the next digit (5) from the dividend to 21 and continue with: 215 / 37

Advancing to step 3:
37 goes into 215 5 times with a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 25.0
If we subtract 185 from 215, we get 30.
Append the next digit (6) from the dividend to 30 and continue with: 306 / 37

Let's proceed to step 4:
37 can be fit into 306 8 times, resulting in a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 258.0
If we take 296 away from 306, we end up with 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 37

Advancing to step 5:
105 divided by 37 is 2 with a remainder of 31.
Record the quotient 2 as the next digit in the result. 
Result so far: 2582.0
Subtracting 74 from 105 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Let's proceed to step 6:
When dividing 310 by 37, we get 8 with a remainder of 14.
The next digit of our result is 8. 
Result so far: 2582.8
If we take 296 away from 310, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
If we divide 140 by 37, we get 3 and a remainder of 29.
Use 3 as the next digit of our solution. 
Result so far: 2582.83
Deduct 111 from 140 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Let's proceed to step 8:
When dividing 290 by 37, we get 7 with a remainder of 31.
Write down 7 as next digit of the result. 
Result so far: 2582.837
If we subtract 259 from 290, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 9:
310 divided by 37 is 8 with a remainder of 14.
Use 8 as the next digit of our solution. 
Result so far: 2582.8378
Deduct 296 from 310 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 10:
140 divided by 37 is 3 with a remainder of 29.
The number 3 becomes the next digit in our result. 
Result so far: 2582.83783
If we subtract 111 from 140, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Going ahead to step 11:
290 divided by 37 is 7 with a remainder of 31.
Write down 7 as next digit of the result. 
Result so far: 2582.837837
Subtract 259 from 290 to get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 12:
The number 37 fits into 310 8 times, leaving a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 2582.8378378
The remainder is 14 after subtracting 296 from 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 13:
If we divide 140 by 37, we get 3 and a remainder of 29.
Write down 3 as next digit of the result. 
Result so far: 2582.83783783
Subtracting 111 from 140 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Our division results in 2582.83783783 with a remaining 2.9e-08.