We look at the division of 13505876 by 126 
The aim is to understand the frequency of 126 in 13505876.

Advancing to step 1:
The number 126 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 126

Let's proceed to step 2:
126 goes into 13 0 times with a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Include the next digit (5) from the dividend after 13, then repeat: 135 / 126

Moving on to step 3:
If we divide 135 by 126, we get 1 and a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 126 from 135 leaves us with 9.
Append the next digit (0) from the dividend to 9 and continue with: 90 / 126

Step 4:
If we divide 90 by 126, we get 0 and a remainder of 90.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Deduct 0 from 90 and we're left with 90.
Bring next digit (5) of the dividend behind the 90 and repeat the process: 905 / 126

Going ahead to step 5:
905 divided by 126 is 7 with a remainder of 23.
Use 7 as the next digit of our solution. 
Result so far: 107.0
Subtracting 882 from 905 leaves us with 23.
Bring next digit (8) of the dividend behind the 23 and repeat the process: 238 / 126

Let's proceed to step 6:
The number 126 fits into 238 1 times, leaving a remainder of 112.
The number 1 becomes the next digit in our result. 
Result so far: 1071.0
Subtracting 126 from 238 leaves us with 112.
Include the next digit (7) from the dividend after 112, then repeat: 1127 / 126

Advancing to step 7:
126 goes into 1127 8 times with a remainder of 119.
Put 8 as the next digit of the answer. 
Result so far: 10718.0
Subtract 1008 from 1127 to get 119.
Bring next digit (6) of the dividend behind the 119 and repeat the process: 1196 / 126

Moving on to step 8:
1196 divided by 126 is 9 with a remainder of 62.
Use 9 as the next digit of our solution. 
Result so far: 107189.0
If we subtract 1134 from 1196, we get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Advancing to step 9:
126 can be fit into 620 4 times, resulting in a remainder of 116.
Use 4 as the next digit of our solution. 
Result so far: 107189.4
If we subtract 504 from 620, we get 116.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1160, and continue the process.

Going ahead to step 10:
When dividing 1160 by 126, we get 9 with a remainder of 26.
Put 9 as the next digit of the answer. 
Result so far: 107189.49
If we subtract 1134 from 1160, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 11:
126 goes into 260 2 times with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 107189.492
Subtract 252 from 260 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 12:
If we divide 80 by 126, we get 0 and a remainder of 80.
The next digit of our result is 0. 
Result so far: 107189.492
Subtracting 0 from 80 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Going ahead to step 13:
800 divided by 126 is 6 with a remainder of 44.
Use 6 as the next digit of our solution. 
Result so far: 107189.49206
Subtracting 756 from 800 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 14:
If we divide 440 by 126, we get 3 and a remainder of 62.
The number 3 becomes the next digit in our result. 
Result so far: 107189.492063
Deduct 378 from 440 and we're left with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Let's proceed to step 15:
If we divide 620 by 126, we get 4 and a remainder of 116.
The next digit of our result is 4. 
Result so far: 107189.4920634
Subtracting 504 from 620 leaves us with 116.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1160, and continue the process.

Moving on to step 16:
If we divide 1160 by 126, we get 9 and a remainder of 26.
Use 9 as the next digit of our solution. 
Result so far: 107189.49206349
Subtract 1134 from 1160 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The quotient of the division is 107189.49206349, and the remainder is 2.6e-08.