We're dividing 153557 by 42 
We're looking to find how many times 42 goes into 153557.

On to step 1:
42 can be fit into 1 0 times, resulting in a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 42

Advancing to step 2:
42 can be fit into 15 0 times, resulting in a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 15, we end up with 15.
Grab the next digit (3) from the dividend, add it to 15, then carry on: 153 / 42

Let's proceed to step 3:
When dividing 153 by 42, we get 3 with a remainder of 27.
Put 3 as the next digit of the answer. 
Result so far: 3.0
The remainder is 27 after subtracting 126 from 153.
Include the next digit (5) from the dividend after 27, then repeat: 275 / 42

Advancing to step 4:
The number 42 fits into 275 6 times, leaving a remainder of 23.
Record the quotient 6 as the next digit in the result. 
Result so far: 36.0
The remainder is 23 after subtracting 252 from 275.
Grab the next digit (5) from the dividend, add it to 23, then carry on: 235 / 42

Step 5:
When dividing 235 by 42, we get 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 365.0
Subtracting 210 from 235 leaves us with 25.
Include the next digit (7) from the dividend after 25, then repeat: 257 / 42

Advancing to step 6:
42 goes into 257 6 times with a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 3656.0
Subtracting 252 from 257 leaves us with 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:
When dividing 50 by 42, we get 1 with a remainder of 8.
Use 1 as the next digit of our solution. 
Result so far: 3656.1
Deduct 42 from 50 and we're left 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.

Advancing to step 8:
42 goes into 80 1 times with a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 3656.11
If we take 42 away from 80, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The quotient of the division is 3656.11, and the remainder is 0.038.