We look at the division of 174464 by 48 
We're looking to find how many times 48 goes into 174464.

Advancing to step 1:
When dividing 1 by 48, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 48

Step 2:
If we divide 17 by 48, we get 0 and a remainder of 17.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Take the next digit (4) from the dividend and append it to 17, then repeat: 174 / 48

On to step 3:
48 goes into 174 3 times with a remainder of 30.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Subtract 144 from 174 to get 30.
Append the next digit (4) from the dividend to 30 and continue with: 304 / 48

Step 4:
The number 48 fits into 304 6 times, leaving a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 36.0
The remainder is 16 after subtracting 288 from 304.
Include the next digit (6) from the dividend after 16, then repeat: 166 / 48

Going ahead to step 5:
48 goes into 166 3 times with a remainder of 22.
Use 3 as the next digit of our solution. 
Result so far: 363.0
Deduct 144 from 166 and we're left with 22.
Fetch the next digit (4) from the dividend, attach it to 22 and continue: 224 / 48

On to step 6:
224 divided by 48 is 4 with a remainder of 32.
Record the quotient 4 as the next digit in the result. 
Result so far: 3634.0
The remainder is 32 after subtracting 192 from 224.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 7:
320 divided by 48 is 6 with a remainder of 32.
Put 6 as the next digit of the answer. 
Result so far: 3634.6
If we subtract 288 from 320, 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.

Moving on to step 8:
320 divided by 48 is 6 with a remainder of 32.
Record the quotient 6 as the next digit in the result. 
Result so far: 3634.66
Deduct 288 from 320 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The quotient of the division is 3634.66, and the remainder is 0.032.