681569 ÷ 61 
We want to figure out the number of times 681569 can be divided by 61.

Moving on to step 1:
61 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 61

Let's proceed to step 2:
61 goes into 68 1 times with a remainder of 7.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 61 from 68 to get 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 61

Advancing to step 3:
When dividing 71 by 61, we get 1 with a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 11.0
If we subtract 61 from 71, we get 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 61

On to step 4:
105 divided by 61 is 1 with a remainder of 44.
Put 1 as the next digit of the answer. 
Result so far: 111.0
Subtracting 61 from 105 leaves us with 44.
Take the next digit (6) from the dividend and append it to 44, then repeat: 446 / 61

Going ahead to step 5:
446 divided by 61 is 7 with a remainder of 19.
Put 7 as the next digit of the answer. 
Result so far: 1117.0
Subtracting 427 from 446 leaves us with 19.
Bring next digit (9) of the dividend behind the 19 and repeat the process: 199 / 61

Let's proceed to step 6:
199 divided by 61 is 3 with a remainder of 16.
Write down 3 as next digit of the result. 
Result so far: 11173.0
Deduct 183 from 199 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
If we divide 160 by 61, we get 2 and a remainder of 38.
Write down 2 as next digit of the result. 
Result so far: 11173.2
If we subtract 122 from 160, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Moving on to step 8:
The number 61 fits into 380 6 times, leaving a remainder of 14.
Record the quotient 6 as the next digit in the result. 
Result so far: 11173.26
The remainder is 14 after subtracting 366 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 9:
140 divided by 61 is 2 with a remainder of 18.
The next digit of our result is 2. 
Result so far: 11173.262
Deduct 122 from 140 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 10:
If we divide 180 by 61, we get 2 and a remainder of 58.
Record the quotient 2 as the next digit in the result. 
Result so far: 11173.2622
Subtract 122 from 180 to get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

The quotient of the division is 11173.2622, and the remainder is 0.00058.