25586 ÷ 37 
Our goal is to divide 25586 by 37.

Let's proceed to step 1:
37 can be fit into 2 0 times, resulting in a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 37

Advancing to step 2:
If we divide 25 by 37, we get 0 and a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Fetch the next digit (5) from the dividend, attach it to 25 and continue: 255 / 37

Advancing to step 3:
37 can be fit into 255 6 times, resulting in a remainder of 33.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 33 after subtracting 222 from 255.
Fetch the next digit (8) from the dividend, attach it to 33 and continue: 338 / 37

Let's proceed to step 4:
If we divide 338 by 37, we get 9 and a remainder of 5.
Use 9 as the next digit of our solution. 
Result so far: 69.0
Deduct 333 from 338 and we're left with 5.
Grab the next digit (6) from the dividend, add it to 5, then carry on: 56 / 37

Advancing to step 5:
37 goes into 56 1 times with a remainder of 19.
The next digit of our result is 1. 
Result so far: 691.0
If we subtract 37 from 56, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 6:
37 can be fit into 190 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 691.5
If we take 185 away from 190, we end up 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 7:
37 goes into 50 1 times with a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 691.51
The remainder is 13 after subtracting 37 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 8:
When dividing 130 by 37, we get 3 with a remainder of 19.
Use 3 as the next digit of our solution. 
Result so far: 691.513
Deduct 111 from 130 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 9:
The number 37 fits into 190 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 691.5135
Subtract 185 from 190 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 10:
37 can be fit into 50 1 times, resulting in a remainder of 13.
The next digit of our result is 1. 
Result so far: 691.51351
The remainder is 13 after subtracting 37 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 11:
If we divide 130 by 37, we get 3 and a remainder of 19.
Write down 3 as next digit of the result. 
Result so far: 691.513513
The remainder is 19 after subtracting 111 from 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 12:
190 divided by 37 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 691.5135135
Subtracting 185 from 190 leaves us 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.

Let's proceed to step 13:
When dividing 50 by 37, we get 1 with a remainder of 13.
The next digit of our result is 1. 
Result so far: 691.51351351
If we subtract 37 from 50, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 691.51351351 with a balance of 1.3e-08.