774346 ÷ 13 
Our goal is to divide 774346 by 13.

On to step 1:
The number 13 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Append the next digit (7) from the dividend to 7 and continue with: 77 / 13

Going ahead to step 2:
When dividing 77 by 13, we get 5 with a remainder of 12.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Deduct 65 from 77 and we're left with 12.
Include the next digit (4) from the dividend after 12, then repeat: 124 / 13

On to step 3:
The number 13 fits into 124 9 times, leaving a remainder of 7.
The next digit of our result is 9. 
Result so far: 59.0
If we take 117 away from 124, we end up with 7.
Append the next digit (3) from the dividend to 7 and continue with: 73 / 13

Advancing to step 4:
When dividing 73 by 13, we get 5 with a remainder of 8.
Use 5 as the next digit of our solution. 
Result so far: 595.0
Deduct 65 from 73 and we're left with 8.
Append the next digit (4) from the dividend to 8 and continue with: 84 / 13

Moving on to step 5:
The number 13 fits into 84 6 times, leaving a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 5956.0
The remainder is 6 after subtracting 78 from 84.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 13

Step 6:
13 can be fit into 66 5 times, resulting in a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 59565.0
Deduct 65 from 66 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.

Let's proceed to step 7:
If we divide 10 by 13, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 59565.0
Subtracting 0 from 10 leaves us 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.

Let's proceed to step 8:
13 goes into 100 7 times with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 59565.07
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 9:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 59565.076
Subtract 78 from 90 to 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.

Let's proceed to step 10:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 59565.0769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 11:
30 divided by 13 is 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 59565.07692
If we subtract 26 from 30, 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.

Advancing to step 12:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 59565.076923
Subtracting 39 from 40 leaves us 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.

Step 13:
13 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 59565.076923
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.

On to step 14:
100 divided by 13 is 7 with a remainder of 9.
The next digit of our result is 7. 
Result so far: 59565.07692307
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

In conclusion, the division gives 59565.07692307 with a balance of 9e-09.