777860 ÷ 45 
Our goal is to divide 777860 by 45.

Going ahead to step 1:
The number 45 fits into 7 0 times, leaving a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 45

Advancing to step 2:
45 can be fit into 77 1 times, resulting in a remainder of 32.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 45 from 77 leaves us with 32.
Grab the next digit (7) from the dividend, add it to 32, then carry on: 327 / 45

Moving on to step 3:
45 goes into 327 7 times with a remainder of 12.
Use 7 as the next digit of our solution. 
Result so far: 17.0
If we subtract 315 from 327, we get 12.
Fetch the next digit (8) from the dividend, attach it to 12 and continue: 128 / 45

Let's proceed to step 4:
The number 45 fits into 128 2 times, leaving a remainder of 38.
Use 2 as the next digit of our solution. 
Result so far: 172.0
Deduct 90 from 128 and we're left with 38.
Append the next digit (6) from the dividend to 38 and continue with: 386 / 45

Advancing to step 5:
45 can be fit into 386 8 times, resulting in a remainder of 26.
Use 8 as the next digit of our solution. 
Result so far: 1728.0
If we subtract 360 from 386, we get 26.
Fetch the next digit (0) from the dividend, attach it to 26 and continue: 260 / 45

Moving on to step 6:
When dividing 260 by 45, we get 5 with a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 17285.0
Subtract 225 from 260 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 7:
The number 45 fits into 350 7 times, leaving a remainder of 35.
Put 7 as the next digit of the answer. 
Result so far: 17285.7
Deduct 315 from 350 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 8:
The number 45 fits into 350 7 times, leaving a remainder of 35.
The number 7 becomes the next digit in our result. 
Result so far: 17285.77
If we take 315 away from 350, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

After the division, we end up with 17285.77 and a remainder of 0.035.