771537 ÷ 19 
Our goal is to divide 771537 by 19.

Advancing to step 1:
19 can be fit into 7 0 times, resulting in a remainder of 7.
The number 0 becomes the next digit in our result. 
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 / 19

Moving on to step 2:
77 divided by 19 is 4 with a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Deduct 76 from 77 and we're left with 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 19

Moving on to step 3:
When dividing 11 by 19, we get 0 with a remainder of 11.
Write down 0 as next digit of the result. 
Result so far: 40.0
If we take 0 away from 11, we end up with 11.
Include the next digit (5) from the dividend after 11, then repeat: 115 / 19

Let's proceed to step 4:
19 goes into 115 6 times with a remainder of 1.
Record the quotient 6 as the next digit in the result. 
Result so far: 406.0
The remainder is 1 after subtracting 114 from 115.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 19

Step 5:
If we divide 13 by 19, we get 0 and a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 4060.0
Subtract 0 from 13 to get 13.
Fetch the next digit (7) from the dividend, attach it to 13 and continue: 137 / 19

On to step 6:
19 goes into 137 7 times with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 40607.0
If we take 133 away from 137, we end up 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.

Moving on to step 7:
The number 19 fits into 40 2 times, leaving a remainder of 2.
The next digit of our result is 2. 
Result so far: 40607.2
Deduct 38 from 40 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
The number 19 fits into 20 1 times, leaving a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 40607.21
Deduct 19 from 20 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 9:
The number 19 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 40607.21
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 10:
When dividing 100 by 19, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 40607.2105
If we subtract 95 from 100, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
50 divided by 19 is 2 with a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 40607.21052
If we subtract 38 from 50, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 12:
19 can be fit into 120 6 times, resulting in a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 40607.210526
If we take 114 away from 120, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 13:
19 can be fit into 60 3 times, resulting in a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 40607.2105263
If we subtract 57 from 60, 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.

Going ahead to step 14:
When dividing 30 by 19, we get 1 with a remainder of 11.
Put 1 as the next digit of the answer. 
Result so far: 40607.21052631
Subtracting 19 from 30 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

In conclusion, the division gives 40607.21052631 with a balance of 1.1e-08.