We look at the division of 174577 by 34 
Our goal is to divide 174577 by 34.

Step 1:
The number 34 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 34

Advancing to step 2:
The number 34 fits into 17 0 times, leaving a remainder of 17.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Bring next digit (4) of the dividend behind the 17 and repeat the process: 174 / 34

Let's proceed to step 3:
174 divided by 34 is 5 with a remainder of 4.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
The remainder is 4 after subtracting 170 from 174.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 34

Moving on to step 4:
34 can be fit into 45 1 times, resulting in a remainder of 11.
The next digit of our result is 1. 
Result so far: 51.0
Subtracting 34 from 45 leaves us with 11.
Fetch the next digit (7) from the dividend, attach it to 11 and continue: 117 / 34

Step 5:
When dividing 117 by 34, we get 3 with a remainder of 15.
Write down 3 as next digit of the result. 
Result so far: 513.0
Subtracting 102 from 117 leaves us with 15.
Include the next digit (7) from the dividend after 15, then repeat: 157 / 34

Advancing to step 6:
When dividing 157 by 34, we get 4 with a remainder of 21.
Write down 4 as next digit of the result. 
Result so far: 5134.0
The remainder is 21 after subtracting 136 from 157.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 7:
The number 34 fits into 210 6 times, leaving a remainder of 6.
The next digit of our result is 6. 
Result so far: 5134.6
If we take 204 away from 210, 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 8:
When dividing 60 by 34, we get 1 with a remainder of 26.
Use 1 as the next digit of our solution. 
Result so far: 5134.61
Subtracting 34 from 60 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 9:
34 goes into 260 7 times with a remainder of 22.
Put 7 as the next digit of the answer. 
Result so far: 5134.617
Subtract 238 from 260 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 10:
When dividing 220 by 34, we get 6 with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 5134.6176
The remainder is 16 after subtracting 204 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 11:
34 goes into 160 4 times with a remainder of 24.
Record the quotient 4 as the next digit in the result. 
Result so far: 5134.61764
Subtract 136 from 160 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 12:
The number 34 fits into 240 7 times, leaving a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 5134.617647
Deduct 238 from 240 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 13:
34 can be fit into 20 0 times, resulting in a remainder of 20.
Record the quotient 0 as the next digit in the result. 
Result so far: 5134.617647
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 14:
If we divide 200 by 34, we get 5 and a remainder of 30.
Put 5 as the next digit of the answer. 
Result so far: 5134.61764705
Subtracting 170 from 200 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 5134.61764705, and the remainder is 3e-08.