634922 ÷ 61 
Our goal is to divide 634922 by 61.

Let's proceed to step 1:
If we divide 6 by 61, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 61

Step 2:
If we divide 63 by 61, we get 1 and a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 61 from 63 and we're left with 2.
Grab the next digit (4) from the dividend, add it to 2, then carry on: 24 / 61

Going ahead to step 3:
61 can be fit into 24 0 times, resulting in a remainder of 24.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 24 after subtracting 0 from 24.
Include the next digit (9) from the dividend after 24, then repeat: 249 / 61

Going ahead to step 4:
249 divided by 61 is 4 with a remainder of 5.
Write down 4 as next digit of the result. 
Result so far: 104.0
If we take 244 away from 249, we end up with 5.
Fetch the next digit (2) from the dividend, attach it to 5 and continue: 52 / 61

Going ahead to step 5:
The number 61 fits into 52 0 times, leaving a remainder of 52.
Write down 0 as next digit of the result. 
Result so far: 1040.0
Deduct 0 from 52 and we're left with 52.
Bring next digit (2) of the dividend behind the 52 and repeat the process: 522 / 61

Advancing to step 6:
If we divide 522 by 61, we get 8 and a remainder of 34.
Put 8 as the next digit of the answer. 
Result so far: 10408.0
Subtract 488 from 522 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 7:
340 divided by 61 is 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 10408.5
Deduct 305 from 340 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 8:
When dividing 350 by 61, we get 5 with a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 10408.55
Deduct 305 from 350 and we're left 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.

The quotient of the division is 10408.55, and the remainder is 0.045.