We look at the division of 137416 by 41 
We're looking to find how many times 41 goes into 137416.

Going ahead to step 1:
41 can be fit into 1 0 times, resulting in a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 41

Going ahead to step 2:
41 can be fit into 13 0 times, resulting in a remainder of 13.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Append the next digit (7) from the dividend to 13 and continue with: 137 / 41

Advancing to step 3:
If we divide 137 by 41, we get 3 and a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 14 after subtracting 123 from 137.
Include the next digit (4) from the dividend after 14, then repeat: 144 / 41

Advancing to step 4:
41 can be fit into 144 3 times, resulting in a remainder of 21.
The number 3 becomes the next digit in our result. 
Result so far: 33.0
Subtracting 123 from 144 leaves us with 21.
Grab the next digit (1) from the dividend, add it to 21, then carry on: 211 / 41

Moving on to step 5:
When dividing 211 by 41, we get 5 with a remainder of 6.
The next digit of our result is 5. 
Result so far: 335.0
Deduct 205 from 211 and we're left with 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 41

Advancing to step 6:
66 divided by 41 is 1 with a remainder of 25.
The next digit of our result is 1. 
Result so far: 3351.0
Subtract 41 from 66 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 7:
250 divided by 41 is 6 with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 3351.6
If we subtract 246 from 250, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
41 goes into 40 0 times with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 3351.6
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 9:
If we divide 400 by 41, we get 9 and a remainder of 31.
The next digit of our result is 9. 
Result so far: 3351.609
If we take 369 away from 400, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Let's proceed to step 10:
When dividing 310 by 41, we get 7 with a remainder of 23.
The next digit of our result is 7. 
Result so far: 3351.6097
The remainder is 23 after subtracting 287 from 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

On to step 11:
41 goes into 230 5 times with a remainder of 25.
The next digit of our result is 5. 
Result so far: 3351.60975
If we subtract 205 from 230, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 12:
41 can be fit into 250 6 times, resulting in a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 3351.609756
Deduct 246 from 250 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 13:
The number 41 fits into 40 0 times, leaving a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 3351.609756
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 14:
The number 41 fits into 400 9 times, leaving a remainder of 31.
The number 9 becomes the next digit in our result. 
Result so far: 3351.60975609
The remainder is 31 after subtracting 369 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Our division results in 3351.60975609 with a remaining 3.1e-08.