We're dividing 646666 by 61 
We want to divide 646666 by 61.

Advancing to step 1:
If we divide 6 by 61, we get 0 and a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 61

Step 2:
If we divide 64 by 61, we get 1 and a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 61 away from 64, we end up with 3.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 61

Step 3:
The number 61 fits into 36 0 times, leaving a remainder of 36.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 36, we end up with 36.
Fetch the next digit (6) from the dividend, attach it to 36 and continue: 366 / 61

Advancing to step 4:
61 can be fit into 366 6 times, resulting in a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 106.0
Subtracting 366 from 366 leaves us with 0.
Fetch the next digit (6) from the dividend, attach it to 0 and continue: 6 / 61

Going ahead to step 5:
When dividing 6 by 61, we get 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 1060.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 61

Let's proceed to step 6:
If we divide 66 by 61, we get 1 and a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 10601.0
Subtract 61 from 66 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 7:
61 can be fit into 50 0 times, resulting in a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 10601.0
Subtracting 0 from 50 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 8:
500 divided by 61 is 8 with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 10601.08
Subtract 488 from 500 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 9:
120 divided by 61 is 1 with a remainder of 59.
Write down 1 as next digit of the result. 
Result so far: 10601.081
Subtracting 61 from 120 leaves us with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 10:
When dividing 590 by 61, we get 9 with a remainder of 41.
Write down 9 as next digit of the result. 
Result so far: 10601.0819
Subtracting 549 from 590 leaves us with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 11:
If we divide 410 by 61, we get 6 and a remainder of 44.
Record the quotient 6 as the next digit in the result. 
Result so far: 10601.08196
Subtracting 366 from 410 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Going ahead to step 12:
If we divide 440 by 61, we get 7 and a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 10601.081967
If we subtract 427 from 440, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 13:
130 divided by 61 is 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 10601.0819672
If we take 122 away from 130, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 14:
61 can be fit into 80 1 times, resulting in a remainder of 19.
Record the quotient 1 as the next digit in the result. 
Result so far: 10601.08196721
If we subtract 61 from 80, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

After the division, we end up with 10601.08196721 and a remainder of 1.9e-08.