We look at the division of 334444 by 3 
We're looking to find how many times 3 goes into 334444.

On to step 1:
When dividing 3 by 3, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 3 from 3 leaves us with 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 3

On to step 2:
3 goes into 3 1 times with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 11.0
The remainder is 0 after subtracting 3 from 3.
Grab the next digit (4) from the dividend, add it to 0, then carry on: 4 / 3

Let's proceed to step 3:
3 goes into 4 1 times with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 111.0
If we subtract 3 from 4, we get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 3

Going ahead to step 4:
3 can be fit into 14 4 times, resulting in a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 1114.0
If we subtract 12 from 14, we get 2.
Grab the next digit (4) from the dividend, add it to 2, then carry on: 24 / 3

Going ahead to step 5:
3 can be fit into 24 8 times, resulting in a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 11148.0
Deduct 24 from 24 and we're left with 0.
Grab the next digit (4) from the dividend, add it to 0, then carry on: 4 / 3

Moving on to step 6:
If we divide 4 by 3, we get 1 and a remainder of 1.
The next digit of our result is 1. 
Result so far: 111481.0
Deduct 3 from 4 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
3 can be fit into 10 3 times, resulting in a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 111481.3
Deduct 9 from 10 and we're left with 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 8:
If we divide 10 by 3, we get 3 and a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 111481.33
Deduct 9 from 10 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Our division results in 111481.33 with a remaining 0.001.