513410 ÷ 87 
We're looking to find how many times 87 goes into 513410.

Step 1:
5 divided by 87 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 87

Step 2:
If we divide 51 by 87, we get 0 and a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Fetch the next digit (3) from the dividend, attach it to 51 and continue: 513 / 87

Moving on to step 3:
513 divided by 87 is 5 with a remainder of 78.
Write down 5 as next digit of the result. 
Result so far: 5.0
Deduct 435 from 513 and we're left with 78.
Fetch the next digit (4) from the dividend, attach it to 78 and continue: 784 / 87

Advancing to step 4:
87 can be fit into 784 9 times, resulting in a remainder of 1.
The next digit of our result is 9. 
Result so far: 59.0
Subtracting 783 from 784 leaves us with 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 87

Moving on to step 5:
87 goes into 11 0 times with a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 590.0
If we take 0 away from 11, we end up with 11.
Include the next digit (0) from the dividend after 11, then repeat: 110 / 87

On to step 6:
The number 87 fits into 110 1 times, leaving a remainder of 23.
The number 1 becomes the next digit in our result. 
Result so far: 5901.0
Deduct 87 from 110 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 7:
When dividing 230 by 87, we get 2 with a remainder of 56.
Write down 2 as next digit of the result. 
Result so far: 5901.2
If we take 174 away from 230, we end up with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Moving on to step 8:
When dividing 560 by 87, we get 6 with a remainder of 38.
Put 6 as the next digit of the answer. 
Result so far: 5901.26
Subtracting 522 from 560 leaves us 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.

Advancing to step 9:
87 can be fit into 380 4 times, resulting in a remainder of 32.
Put 4 as the next digit of the answer. 
Result so far: 5901.264
Subtracting 348 from 380 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 10:
When dividing 320 by 87, we get 3 with a remainder of 59.
Put 3 as the next digit of the answer. 
Result so far: 5901.2643
If we subtract 261 from 320, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 11:
590 divided by 87 is 6 with a remainder of 68.
The next digit of our result is 6. 
Result so far: 5901.26436
The remainder is 68 after subtracting 522 from 590.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Advancing to step 12:
87 goes into 680 7 times with a remainder of 71.
The next digit of our result is 7. 
Result so far: 5901.264367
Subtracting 609 from 680 leaves us with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Moving on to step 13:
When dividing 710 by 87, we get 8 with a remainder of 14.
Record the quotient 8 as the next digit in the result. 
Result so far: 5901.2643678
The remainder is 14 after subtracting 696 from 710.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 14:
87 goes into 140 1 times with a remainder of 53.
Use 1 as the next digit of our solution. 
Result so far: 5901.26436781
If we subtract 87 from 140, we get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

In conclusion, the division gives 5901.26436781 with a balance of 5.3e-08.