3374 ÷ 8 
We're looking to find how many times 8 goes into 3374.

Going ahead to step 1:
If we divide 3 by 8, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (3) from the dividend and append it to 3, then repeat: 33 / 8

Advancing to step 2:
8 can be fit into 33 4 times, resulting in a remainder of 1.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
If we take 32 away from 33, we end up with 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 8

On to step 3:
8 can be fit into 17 2 times, resulting in a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 42.0
If we take 16 away from 17, we end up with 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 8

Let's proceed to step 4:
14 divided by 8 is 1 with a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 421.0
If we take 8 away from 14, we end up 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.

Let's proceed to step 5:
The number 8 fits into 60 7 times, leaving a remainder of 4.
Put 7 as the next digit of the answer. 
Result so far: 421.7
If we subtract 56 from 60, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 6:
8 can be fit into 40 5 times, resulting in a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 421.75
The remainder is 0 after subtracting 40 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 7:
8 can be fit into 0 0 times, resulting in a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 421.75
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
8 can be fit into 0 0 times, resulting in a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 421.75
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 421.75, with a leftover of 0.0.