We're dividing 71417 by 61 
We want to divide 71417 by 61.

Let's proceed to step 1:
If we divide 7 by 61, we get 0 and a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 61

Moving on to step 2:
61 goes into 71 1 times with a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 61 from 71 and we're left with 10.
Include the next digit (4) from the dividend after 10, then repeat: 104 / 61

Let's proceed to step 3:
When dividing 104 by 61, we get 1 with a remainder of 43.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
Subtracting 61 from 104 leaves us with 43.
Append the next digit (1) from the dividend to 43 and continue with: 431 / 61

Let's proceed to step 4:
431 divided by 61 is 7 with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 117.0
The remainder is 4 after subtracting 427 from 431.
Include the next digit (7) from the dividend after 4, then repeat: 47 / 61

Step 5:
If we divide 47 by 61, we get 0 and a remainder of 47.
Put 0 as the next digit of the answer. 
Result so far: 1170.0
If we subtract 0 from 47, we get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Step 6:
61 goes into 470 7 times with a remainder of 43.
Put 7 as the next digit of the answer. 
Result so far: 1170.7
Subtracting 427 from 470 leaves us with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

On to step 7:
If we divide 430 by 61, we get 7 and a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 1170.77
Deduct 427 from 430 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Our division results in 1170.77 with a remaining 0.003.