257637 ÷ 61 
Our goal is to divide 257637 by 61.

Step 1:
61 can be fit into 2 0 times, resulting in a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 61

Going ahead to step 2:
61 can be fit into 25 0 times, resulting in a remainder of 25.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 25 after subtracting 0 from 25.
Grab the next digit (7) from the dividend, add it to 25, then carry on: 257 / 61

Moving on to step 3:
61 can be fit into 257 4 times, resulting in a remainder of 13.
The next digit of our result is 4. 
Result so far: 4.0
The remainder is 13 after subtracting 244 from 257.
Append the next digit (6) from the dividend to 13 and continue with: 136 / 61

Advancing to step 4:
When dividing 136 by 61, we get 2 with a remainder of 14.
The number 2 becomes the next digit in our result. 
Result so far: 42.0
Deduct 122 from 136 and we're left with 14.
Append the next digit (3) from the dividend to 14 and continue with: 143 / 61

Step 5:
143 divided by 61 is 2 with a remainder of 21.
The number 2 becomes the next digit in our result. 
Result so far: 422.0
If we subtract 122 from 143, we get 21.
Append the next digit (7) from the dividend to 21 and continue with: 217 / 61

On to step 6:
When dividing 217 by 61, we get 3 with a remainder of 34.
Write down 3 as next digit of the result. 
Result so far: 4223.0
Deduct 183 from 217 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 7:
When dividing 340 by 61, we get 5 with a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 4223.5
If we take 305 away from 340, we end up 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:
350 divided by 61 is 5 with a remainder of 45.
Write down 5 as next digit of the result. 
Result so far: 4223.55
The remainder is 45 after subtracting 305 from 350.
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 4223.55, and the remainder is 0.045.