We're dividing 21179365 by 513 
We want to figure out the number of times 21179365 can be divided by 513.

Moving on to step 1:
513 goes into 2 0 times with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Take the next digit (1) from the dividend and append it to 2, then repeat: 21 / 513

Advancing to step 2:
If we divide 21 by 513, we get 0 and a remainder of 21.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 21, we get 21.
Fetch the next digit (1) from the dividend, attach it to 21 and continue: 211 / 513

Going ahead to step 3:
If we divide 211 by 513, we get 0 and a remainder of 211.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 211 and we're left with 211.
Fetch the next digit (7) from the dividend, attach it to 211 and continue: 2117 / 513

Let's proceed to step 4:
The number 513 fits into 2117 4 times, leaving a remainder of 65.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we subtract 2052 from 2117, we get 65.
Take the next digit (9) from the dividend and append it to 65, then repeat: 659 / 513

Going ahead to step 5:
513 can be fit into 659 1 times, resulting in a remainder of 146.
Put 1 as the next digit of the answer. 
Result so far: 41.0
Deduct 513 from 659 and we're left with 146.
Bring next digit (3) of the dividend behind the 146 and repeat the process: 1463 / 513

Step 6:
When dividing 1463 by 513, we get 2 with a remainder of 437.
Write down 2 as next digit of the result. 
Result so far: 412.0
Subtract 1026 from 1463 to get 437.
Take the next digit (6) from the dividend and append it to 437, then repeat: 4376 / 513

Let's proceed to step 7:
If we divide 4376 by 513, we get 8 and a remainder of 272.
Write down 8 as next digit of the result. 
Result so far: 4128.0
If we subtract 4104 from 4376, we get 272.
Take the next digit (5) from the dividend and append it to 272, then repeat: 2725 / 513

Let's proceed to step 8:
513 can be fit into 2725 5 times, resulting in a remainder of 160.
Write down 5 as next digit of the result. 
Result so far: 41285.0
If we take 2565 away from 2725, we end up with 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1600, and continue the process.

Let's proceed to step 9:
If we divide 1600 by 513, we get 3 and a remainder of 61.
The next digit of our result is 3. 
Result so far: 41285.3
If we subtract 1539 from 1600, we get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Advancing to step 10:
If we divide 610 by 513, we get 1 and a remainder of 97.
The next digit of our result is 1. 
Result so far: 41285.31
If we take 513 away from 610, we end up with 97.
Since there are no more digits in the dividend, we add a zero to the remainder making it 970, and continue the process.

Advancing to step 11:
970 divided by 513 is 1 with a remainder of 457.
Put 1 as the next digit of the answer. 
Result so far: 41285.311
Deduct 513 from 970 and we're left with 457.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4570, and continue the process.

After the division, we end up with 41285.311 and a remainder of 0.0457.