We're dividing 122633 by 97 
We want to figure out the number of times 122633 can be divided by 97.

On to step 1:
97 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 97

Advancing to step 2:
The number 97 fits into 12 0 times, leaving a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 12 and we're left with 12.
Append the next digit (2) from the dividend to 12 and continue with: 122 / 97

Let's proceed to step 3:
The number 97 fits into 122 1 times, leaving a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 97 from 122 leaves us with 25.
Take the next digit (6) from the dividend and append it to 25, then repeat: 256 / 97

Advancing to step 4:
97 can be fit into 256 2 times, resulting in a remainder of 62.
Write down 2 as next digit of the result. 
Result so far: 12.0
Deduct 194 from 256 and we're left with 62.
Take the next digit (3) from the dividend and append it to 62, then repeat: 623 / 97

Advancing to step 5:
97 can be fit into 623 6 times, resulting in a remainder of 41.
Use 6 as the next digit of our solution. 
Result so far: 126.0
Deduct 582 from 623 and we're left with 41.
Append the next digit (3) from the dividend to 41 and continue with: 413 / 97

Moving on to step 6:
97 goes into 413 4 times with a remainder of 25.
Put 4 as the next digit of the answer. 
Result so far: 1264.0
Subtract 388 from 413 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 7:
If we divide 250 by 97, we get 2 and a remainder of 56.
Use 2 as the next digit of our solution. 
Result so far: 1264.2
Subtract 194 from 250 to get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Going ahead to step 8:
If we divide 560 by 97, we get 5 and a remainder of 75.
Record the quotient 5 as the next digit in the result. 
Result so far: 1264.25
If we take 485 away from 560, we end up with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Moving on to step 9:
When dividing 750 by 97, we get 7 with a remainder of 71.
Write down 7 as next digit of the result. 
Result so far: 1264.257
If we subtract 679 from 750, we get 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Advancing to step 10:
97 can be fit into 710 7 times, resulting in a remainder of 31.
Put 7 as the next digit of the answer. 
Result so far: 1264.2577
If we take 679 away from 710, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

The quotient of the division is 1264.2577, and the remainder is 0.00031.