78814431 ÷ 138 
The aim is to understand the frequency of 138 in 78814431.

Step 1:
If we divide 7 by 138, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Take the next digit (8) from the dividend and append it to 7, then repeat: 78 / 138

Let's proceed to step 2:
138 can be fit into 78 0 times, resulting in a remainder of 78.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 78 to get 78.
Bring next digit (8) of the dividend behind the 78 and repeat the process: 788 / 138

Let's proceed to step 3:
138 can be fit into 788 5 times, resulting in a remainder of 98.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtracting 690 from 788 leaves us with 98.
Bring next digit (1) of the dividend behind the 98 and repeat the process: 981 / 138

Moving on to step 4:
138 goes into 981 7 times with a remainder of 15.
Put 7 as the next digit of the answer. 
Result so far: 57.0
The remainder is 15 after subtracting 966 from 981.
Append the next digit (4) from the dividend to 15 and continue with: 154 / 138

Advancing to step 5:
138 goes into 154 1 times with a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 571.0
Subtract 138 from 154 to get 16.
Append the next digit (4) from the dividend to 16 and continue with: 164 / 138

Going ahead to step 6:
The number 138 fits into 164 1 times, leaving a remainder of 26.
The number 1 becomes the next digit in our result. 
Result so far: 5711.0
Subtract 138 from 164 to get 26.
Append the next digit (3) from the dividend to 26 and continue with: 263 / 138

Let's proceed to step 7:
The number 138 fits into 263 1 times, leaving a remainder of 125.
The number 1 becomes the next digit in our result. 
Result so far: 57111.0
Subtract 138 from 263 to get 125.
Include the next digit (1) from the dividend after 125, then repeat: 1251 / 138

Moving on to step 8:
The number 138 fits into 1251 9 times, leaving a remainder of 9.
Record the quotient 9 as the next digit in the result. 
Result so far: 571119.0
The remainder is 9 after subtracting 1242 from 1251.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 9:
If we divide 90 by 138, we get 0 and a remainder of 90.
The number 0 becomes the next digit in our result. 
Result so far: 571119.0
Deduct 0 from 90 and we're left with 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Moving on to step 10:
138 can be fit into 900 6 times, resulting in a remainder of 72.
Put 6 as the next digit of the answer. 
Result so far: 571119.06
If we subtract 828 from 900, we get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Going ahead to step 11:
138 goes into 720 5 times with a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 571119.065
Subtracting 690 from 720 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 12:
If we divide 300 by 138, we get 2 and a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 571119.0652
Deduct 276 from 300 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 13:
240 divided by 138 is 1 with a remainder of 102.
Use 1 as the next digit of our solution. 
Result so far: 571119.06521
If we subtract 138 from 240, we get 102.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1020, and continue the process.

Step 14:
When dividing 1020 by 138, we get 7 with a remainder of 54.
The number 7 becomes the next digit in our result. 
Result so far: 571119.065217
Subtracting 966 from 1020 leaves us 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.

On to step 15:
138 goes into 540 3 times with a remainder of 126.
The number 3 becomes the next digit in our result. 
Result so far: 571119.0652173
Subtracting 414 from 540 leaves us with 126.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1260, and continue the process.

Advancing to step 16:
138 goes into 1260 9 times with a remainder of 18.
Record the quotient 9 as the next digit in the result. 
Result so far: 571119.06521739
Subtracting 1242 from 1260 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

After the division, we end up with 571119.06521739 and a remainder of 1.8e-08.