10174 ÷ 61 
We want to divide 10174 by 61.

Moving on to step 1:
1 divided by 61 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 61

Moving on to step 2:
10 divided by 61 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Include the next digit (1) from the dividend after 10, then repeat: 101 / 61

Let's proceed to step 3:
When dividing 101 by 61, we get 1 with a remainder of 40.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 61 from 101 leaves us with 40.
Append the next digit (7) from the dividend to 40 and continue with: 407 / 61

Let's proceed to step 4:
When dividing 407 by 61, we get 6 with a remainder of 41.
The next digit of our result is 6. 
Result so far: 16.0
If we take 366 away from 407, we end up with 41.
Append the next digit (4) from the dividend to 41 and continue with: 414 / 61

Advancing to step 5:
61 goes into 414 6 times with a remainder of 48.
The next digit of our result is 6. 
Result so far: 166.0
If we subtract 366 from 414, we get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 6:
When dividing 480 by 61, we get 7 with a remainder of 53.
Record the quotient 7 as the next digit in the result. 
Result so far: 166.7
The remainder is 53 after subtracting 427 from 480.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Let's proceed to step 7:
If we divide 530 by 61, we get 8 and a remainder of 42.
The number 8 becomes the next digit in our result. 
Result so far: 166.78
Subtracting 488 from 530 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 8:
The number 61 fits into 420 6 times, leaving a remainder of 54.
Write down 6 as next digit of the result. 
Result so far: 166.786
Subtract 366 from 420 to get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Advancing to step 9:
540 divided by 61 is 8 with a remainder of 52.
Put 8 as the next digit of the answer. 
Result so far: 166.7868
Deduct 488 from 540 and we're left with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 10:
The number 61 fits into 520 8 times, leaving a remainder of 32.
Record the quotient 8 as the next digit in the result. 
Result so far: 166.78688
Subtract 488 from 520 to 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.

After the division, we end up with 166.78688 and a remainder of 3.2e-05.