136597 divided by 4 
We want to figure out the number of times 136597 can be divided by 4.

Step 1:
If we divide 1 by 4, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 4

On to step 2:
The number 4 fits into 13 3 times, leaving a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we take 12 away from 13, we end up with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 4

Moving on to step 3:
If we divide 16 by 4, we get 4 and a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 34.0
The remainder is 0 after subtracting 16 from 16.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 4

On to step 4:
4 can be fit into 5 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 341.0
Subtracting 4 from 5 leaves us with 1.
Grab the next digit (9) from the dividend, add it to 1, then carry on: 19 / 4

Step 5:
When dividing 19 by 4, we get 4 with a remainder of 3.
Use 4 as the next digit of our solution. 
Result so far: 3414.0
Deduct 16 from 19 and we're left with 3.
Include the next digit (7) from the dividend after 3, then repeat: 37 / 4

Going ahead to step 6:
37 divided by 4 is 9 with a remainder of 1.
The next digit of our result is 9. 
Result so far: 34149.0
If we take 36 away from 37, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
4 goes into 10 2 times with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 34149.2
Subtract 8 from 10 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
When dividing 20 by 4, we get 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 34149.25
If we take 20 away from 20, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 9:
0 divided by 4 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 34149.25
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
4 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 34149.25
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 34149.25 with a remainder of 0.0.