513543 ÷ 59 
We're looking to find how many times 59 goes into 513543.

Moving on to step 1:
When dividing 5 by 59, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 59

Step 2:
When dividing 51 by 59, we get 0 with a remainder of 51.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Bring next digit (3) of the dividend behind the 51 and repeat the process: 513 / 59

Advancing to step 3:
59 can be fit into 513 8 times, resulting in a remainder of 41.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtracting 472 from 513 leaves us with 41.
Fetch the next digit (5) from the dividend, attach it to 41 and continue: 415 / 59

Let's proceed to step 4:
415 divided by 59 is 7 with a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 87.0
Subtracting 413 from 415 leaves us with 2.
Fetch the next digit (4) from the dividend, attach it to 2 and continue: 24 / 59

Going ahead to step 5:
24 divided by 59 is 0 with a remainder of 24.
Put 0 as the next digit of the answer. 
Result so far: 870.0
If we take 0 away from 24, we end up with 24.
Grab the next digit (3) from the dividend, add it to 24, then carry on: 243 / 59

Step 6:
243 divided by 59 is 4 with a remainder of 7.
Write down 4 as next digit of the result. 
Result so far: 8704.0
Deduct 236 from 243 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 7:
When dividing 70 by 59, we get 1 with a remainder of 11.
The next digit of our result is 1. 
Result so far: 8704.1
Subtracting 59 from 70 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 8:
59 can be fit into 110 1 times, resulting in a remainder of 51.
Write down 1 as next digit of the result. 
Result so far: 8704.11
The remainder is 51 after subtracting 59 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

After the division, we end up with 8704.11 and a remainder of 0.051.