81941781 ÷ 603 
We want to figure out the number of times 81941781 can be divided by 603.

On to step 1:
If we divide 8 by 603, we get 0 and a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Fetch the next digit (1) from the dividend, attach it to 8 and continue: 81 / 603

Let's proceed to step 2:
If we divide 81 by 603, we get 0 and a remainder of 81.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 81 and we're left with 81.
Grab the next digit (9) from the dividend, add it to 81, then carry on: 819 / 603

Moving on to step 3:
603 can be fit into 819 1 times, resulting in a remainder of 216.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 603 from 819 and we're left with 216.
Fetch the next digit (4) from the dividend, attach it to 216 and continue: 2164 / 603

Advancing to step 4:
603 goes into 2164 3 times with a remainder of 355.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 1809 away from 2164, we end up with 355.
Append the next digit (1) from the dividend to 355 and continue with: 3551 / 603

On to step 5:
603 can be fit into 3551 5 times, resulting in a remainder of 536.
Use 5 as the next digit of our solution. 
Result so far: 135.0
If we subtract 3015 from 3551, we get 536.
Bring next digit (7) of the dividend behind the 536 and repeat the process: 5367 / 603

Advancing to step 6:
The number 603 fits into 5367 8 times, leaving a remainder of 543.
The next digit of our result is 8. 
Result so far: 1358.0
Deduct 4824 from 5367 and we're left with 543.
Take the next digit (8) from the dividend and append it to 543, then repeat: 5438 / 603

Let's proceed to step 7:
5438 divided by 603 is 9 with a remainder of 11.
The next digit of our result is 9. 
Result so far: 13589.0
Subtracting 5427 from 5438 leaves us with 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 603

Going ahead to step 8:
111 divided by 603 is 0 with a remainder of 111.
Record the quotient 0 as the next digit in the result. 
Result so far: 135890.0
The remainder is 111 after subtracting 0 from 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1110, and continue the process.

Moving on to step 9:
When dividing 1110 by 603, we get 1 with a remainder of 507.
The number 1 becomes the next digit in our result. 
Result so far: 135890.1
Deduct 603 from 1110 and we're left with 507.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5070, and continue the process.

On to step 10:
5070 divided by 603 is 8 with a remainder of 246.
The next digit of our result is 8. 
Result so far: 135890.18
If we take 4824 away from 5070, we end up with 246.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2460, and continue the process.

Moving on to step 11:
603 goes into 2460 4 times with a remainder of 48.
Record the quotient 4 as the next digit in the result. 
Result so far: 135890.184
Subtract 2412 from 2460 to get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 12:
When dividing 480 by 603, we get 0 with a remainder of 480.
The number 0 becomes the next digit in our result. 
Result so far: 135890.184
The remainder is 480 after subtracting 0 from 480.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4800, and continue the process.

Advancing to step 13:
4800 divided by 603 is 7 with a remainder of 579.
The number 7 becomes the next digit in our result. 
Result so far: 135890.18407
Subtracting 4221 from 4800 leaves us with 579.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5790, and continue the process.

Moving on to step 14:
If we divide 5790 by 603, we get 9 and a remainder of 363.
The next digit of our result is 9. 
Result so far: 135890.184079
Subtracting 5427 from 5790 leaves us with 363.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3630, and continue the process.

Advancing to step 15:
3630 divided by 603 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 135890.1840796
Subtracting 3618 from 3630 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 16:
The number 603 fits into 120 0 times, leaving a remainder of 120.
Use 0 as the next digit of our solution. 
Result so far: 135890.1840796
Subtracting 0 from 120 leaves us with 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1200, and continue the process.

After the division, we end up with 135890.1840796 and a remainder of 1.2e-07.