We're dividing 133774 by 97 
We want to figure out the number of times 133774 can be divided by 97.

On to step 1:
When dividing 1 by 97, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 97

Step 2:
If we divide 13 by 97, we get 0 and a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 13 leaves us with 13.
Bring next digit (3) of the dividend behind the 13 and repeat the process: 133 / 97

Advancing to step 3:
When dividing 133 by 97, we get 1 with a remainder of 36.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 36 after subtracting 97 from 133.
Grab the next digit (7) from the dividend, add it to 36, then carry on: 367 / 97

On to step 4:
367 divided by 97 is 3 with a remainder of 76.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtracting 291 from 367 leaves us with 76.
Grab the next digit (7) from the dividend, add it to 76, then carry on: 767 / 97

Step 5:
97 can be fit into 767 7 times, resulting in a remainder of 88.
Record the quotient 7 as the next digit in the result. 
Result so far: 137.0
If we take 679 away from 767, we end up with 88.
Bring next digit (4) of the dividend behind the 88 and repeat the process: 884 / 97

Step 6:
The number 97 fits into 884 9 times, leaving a remainder of 11.
Record the quotient 9 as the next digit in the result. 
Result so far: 1379.0
If we subtract 873 from 884, we 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 7:
110 divided by 97 is 1 with a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 1379.1
If we subtract 97 from 110, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 8:
The number 97 fits into 130 1 times, leaving a remainder of 33.
Write down 1 as next digit of the result. 
Result so far: 1379.11
Deduct 97 from 130 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

The quotient of the division is 1379.11, and the remainder is 0.033.