513105 ÷ 74 
Let's see how many times 74 fits into 513105.

Advancing to step 1:
74 can be fit into 5 0 times, resulting in a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 74

Advancing to step 2:
When dividing 51 by 74, we get 0 with a remainder of 51.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Grab the next digit (3) from the dividend, add it to 51, then carry on: 513 / 74

Step 3:
513 divided by 74 is 6 with a remainder of 69.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 444 from 513, we get 69.
Grab the next digit (1) from the dividend, add it to 69, then carry on: 691 / 74

On to step 4:
74 goes into 691 9 times with a remainder of 25.
Write down 9 as next digit of the result. 
Result so far: 69.0
Deduct 666 from 691 and we're left with 25.
Take the next digit (0) from the dividend and append it to 25, then repeat: 250 / 74

Step 5:
If we divide 250 by 74, we get 3 and a remainder of 28.
Record the quotient 3 as the next digit in the result. 
Result so far: 693.0
If we take 222 away from 250, we end up with 28.
Include the next digit (5) from the dividend after 28, then repeat: 285 / 74

Going ahead to step 6:
74 can be fit into 285 3 times, resulting in a remainder of 63.
The number 3 becomes the next digit in our result. 
Result so far: 6933.0
Subtract 222 from 285 to get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

On to step 7:
74 can be fit into 630 8 times, resulting in a remainder of 38.
The next digit of our result is 8. 
Result so far: 6933.8
Deduct 592 from 630 and we're left 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.

On to step 8:
If we divide 380 by 74, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 6933.85
If we take 370 away from 380, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
74 can be fit into 100 1 times, resulting in a remainder of 26.
Write down 1 as next digit of the result. 
Result so far: 6933.851
The remainder is 26 after subtracting 74 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 10:
When dividing 260 by 74, we get 3 with a remainder of 38.
Use 3 as the next digit of our solution. 
Result so far: 6933.8513
If we take 222 away from 260, 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.

Going ahead to step 11:
74 goes into 380 5 times with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 6933.85135
The remainder is 10 after subtracting 370 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 12:
74 goes into 100 1 times with a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 6933.851351
Subtracting 74 from 100 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 13:
When dividing 260 by 74, we get 3 with a remainder of 38.
Use 3 as the next digit of our solution. 
Result so far: 6933.8513513
If we subtract 222 from 260, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Moving on to step 14:
If we divide 380 by 74, we get 5 and a remainder of 10.
The next digit of our result is 5. 
Result so far: 6933.85135135
If we take 370 away from 380, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Our division results in 6933.85135135 with a remaining 1e-08.