We look at the division of 697666 by 13 
We're looking to find how many times 13 goes into 697666.

Step 1:
If we divide 6 by 13, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (9) from the dividend, add it to 6, then carry on: 69 / 13

On to step 2:
The number 13 fits into 69 5 times, leaving a remainder of 4.
The next digit of our result is 5. 
Result so far: 5.0
If we take 65 away from 69, we end up with 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 13

On to step 3:
If we divide 47 by 13, we get 3 and a remainder of 8.
The next digit of our result is 3. 
Result so far: 53.0
Subtracting 39 from 47 leaves us with 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 13

Moving on to step 4:
The number 13 fits into 86 6 times, leaving a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 536.0
If we take 78 away from 86, we end up with 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 13

On to step 5:
The number 13 fits into 86 6 times, leaving a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 5366.0
Subtract 78 from 86 to get 8.
Append the next digit (6) from the dividend to 8 and continue with: 86 / 13

Moving on to step 6:
13 can be fit into 86 6 times, resulting in a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 53666.0
Deduct 78 from 86 and we're left 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.

On to step 7:
When dividing 80 by 13, we get 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 53666.6
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.

Advancing to step 8:
20 divided by 13 is 1 with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 53666.61
Deduct 13 from 20 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 9:
70 divided by 13 is 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 53666.615
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.

Let's proceed to step 10:
13 can be fit into 50 3 times, resulting in a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 53666.6153
If we take 39 away from 50, 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.

On to step 11:
When dividing 110 by 13, we get 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 53666.61538
If we subtract 104 from 110, we get 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 12:
When dividing 60 by 13, we get 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 53666.615384
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.

Moving on to step 13:
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: 53666.6153846
If we take 78 away from 80, we end up 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 14:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 53666.61538461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The quotient of the division is 53666.61538461, and the remainder is 7e-09.