We're dividing 137309 by 4 
The aim is to understand the frequency of 4 in 137309.

Let's proceed to step 1:
When dividing 1 by 4, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 4

Moving on to step 2:
4 can be fit into 13 3 times, resulting in a remainder of 1.
The next digit of our result is 3. 
Result so far: 3.0
Subtract 12 from 13 to get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 4

Let's proceed to step 3:
4 can be fit into 17 4 times, resulting in a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 34.0
Subtracting 16 from 17 leaves us with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 4

Moving on to step 4:
4 goes into 13 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 343.0
If we take 12 away from 13, we end up with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 4

Step 5:
When dividing 10 by 4, we get 2 with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 3432.0
Deduct 8 from 10 and we're left with 2.
Take the next digit (9) from the dividend and append it to 2, then repeat: 29 / 4

Moving on to step 6:
29 divided by 4 is 7 with a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 34327.0
The remainder is 1 after subtracting 28 from 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead 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: 34327.2
The remainder is 2 after subtracting 8 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
The number 4 fits into 20 5 times, leaving a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 34327.25
Subtracting 20 from 20 leaves us 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.

Going ahead to step 9:
The number 4 fits into 0 0 times, leaving a remainder of 0.
The next digit of our result is 0. 
Result so far: 34327.25
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.

Moving on to step 10:
0 divided by 4 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 34327.25
Subtracting 0 from 0 leaves us 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 quotient of the division is 34327.25, and the remainder is 0.0.