597136 ÷ 59 
The aim is to understand the frequency of 59 in 597136.

Let's proceed to step 1:
If we divide 5 by 59, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 59

Advancing to step 2:
When dividing 59 by 59, we get 1 with a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 59 from 59 to get 0.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 59

On to step 3:
59 goes into 7 0 times with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtracting 0 from 7 leaves us with 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 59

Advancing to step 4:
59 can be fit into 71 1 times, resulting in a remainder of 12.
The number 1 becomes the next digit in our result. 
Result so far: 101.0
If we subtract 59 from 71, we get 12.
Append the next digit (3) from the dividend to 12 and continue with: 123 / 59

On to step 5:
The number 59 fits into 123 2 times, leaving a remainder of 5.
Record the quotient 2 as the next digit in the result. 
Result so far: 1012.0
Subtract 118 from 123 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 59

On to step 6:
If we divide 56 by 59, we get 0 and a remainder of 56.
Use 0 as the next digit of our solution. 
Result so far: 10120.0
Subtracting 0 from 56 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Moving on to step 7:
59 goes into 560 9 times with a remainder of 29.
Write down 9 as next digit of the result. 
Result so far: 10120.9
If we subtract 531 from 560, 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.

Moving on to step 8:
If we divide 290 by 59, we get 4 and a remainder of 54.
The number 4 becomes the next digit in our result. 
Result so far: 10120.94
If we take 236 away from 290, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Step 9:
540 divided by 59 is 9 with a remainder of 9.
The next digit of our result is 9. 
Result so far: 10120.949
Deduct 531 from 540 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 10:
When dividing 90 by 59, we get 1 with a remainder of 31.
Write down 1 as next digit of the result. 
Result so far: 10120.9491
Subtracting 59 from 90 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.

On to step 11:
59 goes into 310 5 times with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 10120.94915
The remainder is 15 after subtracting 295 from 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 12:
If we divide 150 by 59, we get 2 and a remainder of 32.
Record the quotient 2 as the next digit in the result. 
Result so far: 10120.949152
Subtract 118 from 150 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 13:
The number 59 fits into 320 5 times, leaving a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 10120.9491525
Deduct 295 from 320 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 14:
The number 59 fits into 250 4 times, leaving a remainder of 14.
Use 4 as the next digit of our solution. 
Result so far: 10120.94915254
If we subtract 236 from 250, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

In conclusion, the division gives 10120.94915254 with a balance of 1.4e-08.