677688 ÷ 13 
We want to figure out the number of times 677688 can be divided by 13.

Let's proceed to step 1:
The number 13 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Grab the next digit (7) from the dividend, add it to 6, then carry on: 67 / 13

Moving on to step 2:
If we divide 67 by 13, we get 5 and a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 65 from 67 leaves us with 2.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 13

Moving on to step 3:
The number 13 fits into 27 2 times, leaving a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 52.0
Deduct 26 from 27 and we're left with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 13

On to step 4:
When dividing 16 by 13, we get 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 521.0
Deduct 13 from 16 and we're left with 3.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 13

Step 5:
The number 13 fits into 38 2 times, leaving a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 5212.0
Subtract 26 from 38 to get 12.
Take the next digit (8) from the dividend and append it to 12, then repeat: 128 / 13

On to step 6:
13 can be fit into 128 9 times, resulting in a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 52129.0
If we take 117 away from 128, we end up 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.

Let's proceed to step 7:
When dividing 110 by 13, we get 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 52129.8
If we take 104 away from 110, 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.

Moving on to step 8:
If we divide 60 by 13, we get 4 and a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 52129.84
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
When dividing 80 by 13, we get 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 52129.846
Subtracting 78 from 80 leaves us 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.

Step 10:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 52129.8461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 11:
13 can be fit into 70 5 times, resulting in a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 52129.84615
Deduct 65 from 70 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 12:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 52129.846153
Subtract 39 from 50 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 13:
If we divide 110 by 13, we get 8 and a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 52129.8461538
Deduct 104 from 110 and we're left 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.

Going ahead to step 14:
60 divided by 13 is 4 with a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 52129.84615384
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

In conclusion, the division gives 52129.84615384 with a balance of 8e-09.