We're dividing 106 by 61 
We want to divide 106 by 61.

Step 1:
The number 61 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 61

Step 2:
If we divide 10 by 61, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Bring next digit (6) of the dividend behind the 10 and repeat the process: 106 / 61

Step 3:
61 goes into 106 1 times with a remainder of 45.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 61 from 106 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Step 4:
61 goes into 450 7 times with a remainder of 23.
Use 7 as the next digit of our solution. 
Result so far: 1.7
If we take 427 away from 450, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 5:
230 divided by 61 is 3 with a remainder of 47.
Use 3 as the next digit of our solution. 
Result so far: 1.73
If we subtract 183 from 230, 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.

Moving on to step 6:
The number 61 fits into 470 7 times, leaving a remainder of 43.
Put 7 as the next digit of the answer. 
Result so far: 1.737
If we subtract 427 from 470, we get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Going ahead to step 7:
430 divided by 61 is 7 with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 1.7377
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.

The quotient of the division is 1.7377, and the remainder is 3e-05.