We look at the division of 953538 by 61 
We're looking to find how many times 61 goes into 953538.

On to step 1:
The number 61 fits into 9 0 times, leaving a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Take the next digit (5) from the dividend and append it to 9, then repeat: 95 / 61

On to step 2:
When dividing 95 by 61, we get 1 with a remainder of 34.
The next digit of our result is 1. 
Result so far: 1.0
If we take 61 away from 95, we end up with 34.
Bring next digit (3) of the dividend behind the 34 and repeat the process: 343 / 61

On to step 3:
61 can be fit into 343 5 times, resulting in a remainder of 38.
Write down 5 as next digit of the result. 
Result so far: 15.0
If we subtract 305 from 343, we get 38.
Fetch the next digit (5) from the dividend, attach it to 38 and continue: 385 / 61

Advancing to step 4:
385 divided by 61 is 6 with a remainder of 19.
The next digit of our result is 6. 
Result so far: 156.0
If we take 366 away from 385, we end up with 19.
Include the next digit (3) from the dividend after 19, then repeat: 193 / 61

Moving on to step 5:
The number 61 fits into 193 3 times, leaving a remainder of 10.
Write down 3 as next digit of the result. 
Result so far: 1563.0
The remainder is 10 after subtracting 183 from 193.
Include the next digit (8) from the dividend after 10, then repeat: 108 / 61

On to step 6:
108 divided by 61 is 1 with a remainder of 47.
Record the quotient 1 as the next digit in the result. 
Result so far: 15631.0
If we take 61 away from 108, we end up with 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 7:
The number 61 fits into 470 7 times, leaving a remainder of 43.
The number 7 becomes the next digit in our result. 
Result so far: 15631.7
Subtracting 427 from 470 leaves us with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Advancing to step 8:
430 divided by 61 is 7 with a remainder of 3.
The next digit of our result is 7. 
Result so far: 15631.77
If we subtract 427 from 430, we get 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 15631.77, and the remainder is 0.003.