We look at the division of 771806 by 603 
We want to figure out the number of times 771806 can be divided by 603.

On to step 1:
If we divide 7 by 603, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 603

Advancing to step 2:
77 divided by 603 is 0 with a remainder of 77.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 77, we end up with 77.
Append the next digit (1) from the dividend to 77 and continue with: 771 / 603

Step 3:
When dividing 771 by 603, we get 1 with a remainder of 168.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 603 from 771 and we're left with 168.
Take the next digit (8) from the dividend and append it to 168, then repeat: 1688 / 603

On to step 4:
If we divide 1688 by 603, we get 2 and a remainder of 482.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
If we take 1206 away from 1688, we end up with 482.
Grab the next digit (0) from the dividend, add it to 482, then carry on: 4820 / 603

Advancing to step 5:
The number 603 fits into 4820 7 times, leaving a remainder of 599.
The next digit of our result is 7. 
Result so far: 127.0
If we take 4221 away from 4820, we end up with 599.
Grab the next digit (6) from the dividend, add it to 599, then carry on: 5996 / 603

Going ahead to step 6:
5996 divided by 603 is 9 with a remainder of 569.
Write down 9 as next digit of the result. 
Result so far: 1279.0
The remainder is 569 after subtracting 5427 from 5996.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5690, and continue the process.

Advancing to step 7:
603 can be fit into 5690 9 times, resulting in a remainder of 263.
Put 9 as the next digit of the answer. 
Result so far: 1279.9
The remainder is 263 after subtracting 5427 from 5690.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2630, and continue the process.

Step 8:
If we divide 2630 by 603, we get 4 and a remainder of 218.
Use 4 as the next digit of our solution. 
Result so far: 1279.94
If we subtract 2412 from 2630, we get 218.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2180, and continue the process.

Advancing to step 9:
If we divide 2180 by 603, we get 3 and a remainder of 371.
The number 3 becomes the next digit in our result. 
Result so far: 1279.943
If we subtract 1809 from 2180, we get 371.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3710, and continue the process.

Step 10:
The number 603 fits into 3710 6 times, leaving a remainder of 92.
Write down 6 as next digit of the result. 
Result so far: 1279.9436
If we subtract 3618 from 3710, we get 92.
Since there are no more digits in the dividend, we add a zero to the remainder making it 920, and continue the process.

Advancing to step 11:
When dividing 920 by 603, we get 1 with a remainder of 317.
The number 1 becomes the next digit in our result. 
Result so far: 1279.94361
Deduct 603 from 920 and we're left with 317.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3170, and continue the process.

Step 12:
When dividing 3170 by 603, we get 5 with a remainder of 155.
Put 5 as the next digit of the answer. 
Result so far: 1279.943615
Deduct 3015 from 3170 and we're left with 155.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1550, and continue the process.

Let's proceed to step 13:
1550 divided by 603 is 2 with a remainder of 344.
Record the quotient 2 as the next digit in the result. 
Result so far: 1279.9436152
The remainder is 344 after subtracting 1206 from 1550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3440, and continue the process.

On to step 14:
603 can be fit into 3440 5 times, resulting in a remainder of 425.
Record the quotient 5 as the next digit in the result. 
Result so far: 1279.94361525
Deduct 3015 from 3440 and we're left with 425.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4250, and continue the process.

Our division results in 1279.94361525 with a remaining 4.25e-07.