4600 ÷ 61 
We want to divide 4600 by 61.

Step 1:
61 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 61

Step 2:
61 goes into 46 0 times with a remainder of 46.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 46, we end up with 46.
Bring next digit (0) of the dividend behind the 46 and repeat the process: 460 / 61

Step 3:
If we divide 460 by 61, we get 7 and a remainder of 33.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Deduct 427 from 460 and we're left with 33.
Append the next digit (0) from the dividend to 33 and continue with: 330 / 61

Step 4:
61 can be fit into 330 5 times, resulting in a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 75.0
If we subtract 305 from 330, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 5:
61 can be fit into 250 4 times, resulting in a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 75.4
If we take 244 away from 250, 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.

Going ahead to step 6:
61 goes into 60 0 times with a remainder of 60.
Use 0 as the next digit of our solution. 
Result so far: 75.4
If we subtract 0 from 60, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 7:
61 goes into 600 9 times with a remainder of 51.
Write down 9 as next digit of the result. 
Result so far: 75.409
Deduct 549 from 600 and we're left with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Moving on to step 8:
The number 61 fits into 510 8 times, leaving a remainder of 22.
The next digit of our result is 8. 
Result so far: 75.4098
Subtracting 488 from 510 leaves us with 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 9:
61 can be fit into 220 3 times, resulting in a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 75.40983
The remainder is 37 after subtracting 183 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Let's proceed to step 10:
If we divide 370 by 61, we get 6 and a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 75.409836
If we subtract 366 from 370, we get 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 11:
When dividing 40 by 61, we get 0 with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 75.409836
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 12:
The number 61 fits into 400 6 times, leaving a remainder of 34.
The next digit of our result is 6. 
Result so far: 75.40983606
The remainder is 34 after subtracting 366 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

The quotient of the division is 75.40983606, and the remainder is 3.4e-08.