We look at the division of 4557 by 34 
We want to figure out the number of times 4557 can be divided by 34.

Moving on to step 1:
34 goes into 4 0 times with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 34

Advancing to step 2:
34 goes into 45 1 times with a remainder of 11.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 11 after subtracting 34 from 45.
Take the next digit (5) from the dividend and append it to 11, then repeat: 115 / 34

Moving on to step 3:
34 goes into 115 3 times with a remainder of 13.
Write down 3 as next digit of the result. 
Result so far: 13.0
Subtracting 102 from 115 leaves us with 13.
Fetch the next digit (7) from the dividend, attach it to 13 and continue: 137 / 34

On to step 4:
34 can be fit into 137 4 times, resulting in a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 134.0
Deduct 136 from 137 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 5:
34 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 134.0
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 6:
If we divide 100 by 34, we get 2 and a remainder of 32.
Use 2 as the next digit of our solution. 
Result so far: 134.02
If we subtract 68 from 100, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 7:
If we divide 320 by 34, we get 9 and a remainder of 14.
Put 9 as the next digit of the answer. 
Result so far: 134.029
If we subtract 306 from 320, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 8:
34 goes into 140 4 times with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 134.0294
If we take 136 away from 140, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 9:
34 goes into 40 1 times with a remainder of 6.
The next digit of our result is 1. 
Result so far: 134.02941
The remainder is 6 after subtracting 34 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 10:
34 goes into 60 1 times with a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 134.029411
If we subtract 34 from 60, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Our division results in 134.029411 with a remaining 2.6e-06.