7671 ÷ 63 
We want to figure out the number of times 7671 can be divided by 63.

On to step 1:
If we divide 7 by 63, we get 0 and a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 63

Step 2:
63 can be fit into 76 1 times, resulting in a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 63 away from 76, we end up with 13.
Fetch the next digit (7) from the dividend, attach it to 13 and continue: 137 / 63

Moving on to step 3:
When dividing 137 by 63, we get 2 with a remainder of 11.
The next digit of our result is 2. 
Result so far: 12.0
Subtract 126 from 137 to get 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 63

Advancing to step 4:
111 divided by 63 is 1 with a remainder of 48.
Use 1 as the next digit of our solution. 
Result so far: 121.0
The remainder is 48 after subtracting 63 from 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Advancing to step 5:
63 goes into 480 7 times with a remainder of 39.
Put 7 as the next digit of the answer. 
Result so far: 121.7
If we take 441 away from 480, we end up with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Step 6:
390 divided by 63 is 6 with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 121.76
If we take 378 away from 390, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 7:
63 can be fit into 120 1 times, resulting in a remainder of 57.
The number 1 becomes the next digit in our result. 
Result so far: 121.761
The remainder is 57 after subtracting 63 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

On to step 8:
The number 63 fits into 570 9 times, leaving a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 121.7619
If we take 567 away from 570, we end up 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.

Let's proceed to step 9:
If we divide 30 by 63, we get 0 and a remainder of 30.
The next digit of our result is 0. 
Result so far: 121.7619
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 10:
63 goes into 300 4 times with a remainder of 48.
The next digit of our result is 4. 
Result so far: 121.761904
Deduct 252 from 300 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Advancing to step 11:
When dividing 480 by 63, we get 7 with a remainder of 39.
Put 7 as the next digit of the answer. 
Result so far: 121.7619047
Deduct 441 from 480 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Going ahead to step 12:
390 divided by 63 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 121.76190476
Deduct 378 from 390 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Our division results in 121.76190476 with a remaining 1.2e-08.