25888911 ÷ 688 
The aim is to understand the frequency of 688 in 25888911.

Advancing to step 1:
2 divided by 688 is 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 688

On to step 2:
If we divide 25 by 688, we get 0 and a remainder of 25.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 25 leaves us with 25.
Take the next digit (8) from the dividend and append it to 25, then repeat: 258 / 688

Step 3:
When dividing 258 by 688, we get 0 with a remainder of 258.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 258 leaves us with 258.
Grab the next digit (8) from the dividend, add it to 258, then carry on: 2588 / 688

Moving on to step 4:
2588 divided by 688 is 3 with a remainder of 524.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Deduct 2064 from 2588 and we're left with 524.
Fetch the next digit (8) from the dividend, attach it to 524 and continue: 5248 / 688

Moving on to step 5:
When dividing 5248 by 688, we get 7 with a remainder of 432.
Put 7 as the next digit of the answer. 
Result so far: 37.0
The remainder is 432 after subtracting 4816 from 5248.
Grab the next digit (9) from the dividend, add it to 432, then carry on: 4329 / 688

On to step 6:
If we divide 4329 by 688, we get 6 and a remainder of 201.
Record the quotient 6 as the next digit in the result. 
Result so far: 376.0
If we take 4128 away from 4329, we end up with 201.
Take the next digit (1) from the dividend and append it to 201, then repeat: 2011 / 688

Step 7:
688 can be fit into 2011 2 times, resulting in a remainder of 635.
Record the quotient 2 as the next digit in the result. 
Result so far: 3762.0
Subtracting 1376 from 2011 leaves us with 635.
Fetch the next digit (1) from the dividend, attach it to 635 and continue: 6351 / 688

Going ahead to step 8:
If we divide 6351 by 688, we get 9 and a remainder of 159.
Put 9 as the next digit of the answer. 
Result so far: 37629.0
If we subtract 6192 from 6351, we get 159.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1590, and continue the process.

Going ahead to step 9:
When dividing 1590 by 688, we get 2 with a remainder of 214.
The number 2 becomes the next digit in our result. 
Result so far: 37629.2
Subtracting 1376 from 1590 leaves us with 214.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2140, and continue the process.

Step 10:
2140 divided by 688 is 3 with a remainder of 76.
Put 3 as the next digit of the answer. 
Result so far: 37629.23
Subtracting 2064 from 2140 leaves us with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Step 11:
When dividing 760 by 688, we get 1 with a remainder of 72.
The number 1 becomes the next digit in our result. 
Result so far: 37629.231
Deduct 688 from 760 and we're left with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Advancing to step 12:
688 goes into 720 1 times with a remainder of 32.
Put 1 as the next digit of the answer. 
Result so far: 37629.2311
If we take 688 away from 720, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The quotient of the division is 37629.2311, and the remainder is 0.00032.