975690 ÷ 41 
Our goal is to divide 975690 by 41.

Advancing to step 1:
41 goes into 9 0 times with a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 9, we end up with 9.
Include the next digit (7) from the dividend after 9, then repeat: 97 / 41

Moving on to step 2:
97 divided by 41 is 2 with a remainder of 15.
Put 2 as the next digit of the answer. 
Result so far: 2.0
The remainder is 15 after subtracting 82 from 97.
Take the next digit (5) from the dividend and append it to 15, then repeat: 155 / 41

Going ahead to step 3:
41 can be fit into 155 3 times, resulting in a remainder of 32.
Record the quotient 3 as the next digit in the result. 
Result so far: 23.0
Subtracting 123 from 155 leaves us with 32.
Include the next digit (6) from the dividend after 32, then repeat: 326 / 41

Moving on to step 4:
The number 41 fits into 326 7 times, leaving a remainder of 39.
Write down 7 as next digit of the result. 
Result so far: 237.0
Deduct 287 from 326 and we're left with 39.
Include the next digit (9) from the dividend after 39, then repeat: 399 / 41

Let's proceed to step 5:
The number 41 fits into 399 9 times, leaving a remainder of 30.
Use 9 as the next digit of our solution. 
Result so far: 2379.0
If we take 369 away from 399, we end up with 30.
Include the next digit (0) from the dividend after 30, then repeat: 300 / 41

Step 6:
300 divided by 41 is 7 with a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 23797.0
Deduct 287 from 300 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 7:
130 divided by 41 is 3 with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 23797.3
Deduct 123 from 130 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
70 divided by 41 is 1 with a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 23797.31
Subtracting 41 from 70 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 9:
41 can be fit into 290 7 times, resulting in a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 23797.317
If we subtract 287 from 290, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 10:
41 can be fit into 30 0 times, resulting in a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 23797.317
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 11:
If we divide 300 by 41, we get 7 and a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 23797.31707
If we subtract 287 from 300, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 12:
When dividing 130 by 41, we get 3 with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 23797.317073
If we subtract 123 from 130, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 13:
The number 41 fits into 70 1 times, leaving a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 23797.3170731
Subtract 41 from 70 to get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 14:
The number 41 fits into 290 7 times, leaving a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 23797.31707317
If we take 287 away from 290, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Our division results in 23797.31707317 with a remaining 3e-09.