We look at the division of 5645 by 7 
We want to figure out the number of times 5645 can be divided by 7.

Advancing to step 1:
7 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 7

Moving on to step 2:
When dividing 56 by 7, we get 8 with a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
The remainder is 0 after subtracting 56 from 56.
Append the next digit (4) from the dividend to 0 and continue with: 4 / 7

On to step 3:
The number 7 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 80.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 7

Advancing to step 4:
If we divide 45 by 7, we get 6 and a remainder of 3.
Record the quotient 6 as the next digit in the result. 
Result so far: 806.0
Subtracting 42 from 45 leaves us with 3.
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 5:
7 can be fit into 30 4 times, resulting in a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 806.4
If we take 28 away from 30, 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 6:
If we divide 20 by 7, we get 2 and a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 806.42
Subtract 14 from 20 to 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 7:
When dividing 60 by 7, we get 8 with a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 806.428
Subtracting 56 from 60 leaves us 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 8:
40 divided by 7 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 806.4285
If we subtract 35 from 40, 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.

On to step 9:
7 goes into 50 7 times with a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 806.42857
Subtract 49 from 50 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 10:
If we divide 10 by 7, we get 1 and a remainder of 3.
The next digit of our result is 1. 
Result so far: 806.428571
Subtracting 7 from 10 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 11:
7 goes into 30 4 times with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 806.4285714
Subtracting 28 from 30 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.

Moving on to step 12:
7 can be fit into 20 2 times, resulting in a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 806.42857142
Deduct 14 from 20 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.

The final result is 806.42857142 with a remainder of 6e-09.