40971589 divided by 523 
The aim is to understand the frequency of 523 in 40971589.

Going ahead to step 1:
4 divided by 523 is 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 523

Advancing to step 2:
523 can be fit into 40 0 times, resulting in a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 40 and we're left with 40.
Include the next digit (9) from the dividend after 40, then repeat: 409 / 523

Advancing to step 3:
523 can be fit into 409 0 times, resulting in a remainder of 409.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 409 after subtracting 0 from 409.
Bring next digit (7) of the dividend behind the 409 and repeat the process: 4097 / 523

Step 4:
When dividing 4097 by 523, we get 7 with a remainder of 436.
The next digit of our result is 7. 
Result so far: 7.0
Deduct 3661 from 4097 and we're left with 436.
Bring next digit (1) of the dividend behind the 436 and repeat the process: 4361 / 523

Moving on to step 5:
523 goes into 4361 8 times with a remainder of 177.
The next digit of our result is 8. 
Result so far: 78.0
The remainder is 177 after subtracting 4184 from 4361.
Take the next digit (5) from the dividend and append it to 177, then repeat: 1775 / 523

Advancing to step 6:
When dividing 1775 by 523, we get 3 with a remainder of 206.
Write down 3 as next digit of the result. 
Result so far: 783.0
Subtracting 1569 from 1775 leaves us with 206.
Append the next digit (8) from the dividend to 206 and continue with: 2068 / 523

Let's proceed to step 7:
2068 divided by 523 is 3 with a remainder of 499.
The next digit of our result is 3. 
Result so far: 7833.0
The remainder is 499 after subtracting 1569 from 2068.
Take the next digit (9) from the dividend and append it to 499, then repeat: 4999 / 523

On to step 8:
4999 divided by 523 is 9 with a remainder of 292.
The next digit of our result is 9. 
Result so far: 78339.0
If we take 4707 away from 4999, we end up with 292.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2920, and continue the process.

Advancing to step 9:
The number 523 fits into 2920 5 times, leaving a remainder of 305.
The number 5 becomes the next digit in our result. 
Result so far: 78339.5
Subtract 2615 from 2920 to get 305.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3050, and continue the process.

Let's proceed to step 10:
The number 523 fits into 3050 5 times, leaving a remainder of 435.
Put 5 as the next digit of the answer. 
Result so far: 78339.55
If we take 2615 away from 3050, we end up with 435.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4350, and continue the process.

After the division, we end up with 78339.55 and a remainder of 0.435.