7142613 ÷ 653 
The aim is to understand the frequency of 653 in 7142613.

On to step 1:
The number 653 fits into 7 0 times, leaving a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 653

Moving on to step 2:
71 divided by 653 is 0 with a remainder of 71.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 71 to get 71.
Fetch the next digit (4) from the dividend, attach it to 71 and continue: 714 / 653

On to step 3:
If we divide 714 by 653, we get 1 and a remainder of 61.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 653 from 714 to get 61.
Bring next digit (2) of the dividend behind the 61 and repeat the process: 612 / 653

Step 4:
653 can be fit into 612 0 times, resulting in a remainder of 612.
Put 0 as the next digit of the answer. 
Result so far: 10.0
Deduct 0 from 612 and we're left with 612.
Fetch the next digit (6) from the dividend, attach it to 612 and continue: 6126 / 653

Moving on to step 5:
When dividing 6126 by 653, we get 9 with a remainder of 249.
Record the quotient 9 as the next digit in the result. 
Result so far: 109.0
Deduct 5877 from 6126 and we're left with 249.
Bring next digit (1) of the dividend behind the 249 and repeat the process: 2491 / 653

On to step 6:
653 can be fit into 2491 3 times, resulting in a remainder of 532.
The next digit of our result is 3. 
Result so far: 1093.0
Deduct 1959 from 2491 and we're left with 532.
Take the next digit (3) from the dividend and append it to 532, then repeat: 5323 / 653

Going ahead to step 7:
When dividing 5323 by 653, we get 8 with a remainder of 99.
Write down 8 as next digit of the result. 
Result so far: 10938.0
Deduct 5224 from 5323 and we're left with 99.
Since there are no more digits in the dividend, we add a zero to the remainder making it 990, and continue the process.

Let's proceed to step 8:
If we divide 990 by 653, we get 1 and a remainder of 337.
Record the quotient 1 as the next digit in the result. 
Result so far: 10938.1
If we take 653 away from 990, we end up with 337.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3370, and continue the process.

Step 9:
653 can be fit into 3370 5 times, resulting in a remainder of 105.
Put 5 as the next digit of the answer. 
Result so far: 10938.15
If we take 3265 away from 3370, we end up with 105.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1050, and continue the process.

On to step 10:
The number 653 fits into 1050 1 times, leaving a remainder of 397.
Write down 1 as next digit of the result. 
Result so far: 10938.151
Subtracting 653 from 1050 leaves us with 397.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3970, and continue the process.

Let's proceed to step 11:
653 can be fit into 3970 6 times, resulting in a remainder of 52.
Use 6 as the next digit of our solution. 
Result so far: 10938.1516
The remainder is 52 after subtracting 3918 from 3970.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 12:
The number 653 fits into 520 0 times, leaving a remainder of 520.
Record the quotient 0 as the next digit in the result. 
Result so far: 10938.1516
If we subtract 0 from 520, we get 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5200, and continue the process.

On to step 13:
The number 653 fits into 5200 7 times, leaving a remainder of 629.
Put 7 as the next digit of the answer. 
Result so far: 10938.151607
Subtract 4571 from 5200 to get 629.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6290, and continue the process.

Moving on to step 14:
The number 653 fits into 6290 9 times, leaving a remainder of 413.
The number 9 becomes the next digit in our result. 
Result so far: 10938.1516079
Subtract 5877 from 6290 to get 413.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4130, and continue the process.

Moving on to step 15:
The number 653 fits into 4130 6 times, leaving a remainder of 212.
Write down 6 as next digit of the result. 
Result so far: 10938.15160796
Subtracting 3918 from 4130 leaves us with 212.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2120, and continue the process.

The final outcome is 10938.15160796, with a leftover of 2.12e-07.