61780431 ÷ 513 
The aim is to understand the frequency of 513 in 61780431.

Going ahead to step 1:
513 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Include the next digit (1) from the dividend after 6, then repeat: 61 / 513

On to step 2:
513 can be fit into 61 0 times, resulting in a remainder of 61.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 61, we get 61.
Grab the next digit (7) from the dividend, add it to 61, then carry on: 617 / 513

Going ahead to step 3:
617 divided by 513 is 1 with a remainder of 104.
The next digit of our result is 1. 
Result so far: 1.0
If we take 513 away from 617, we end up with 104.
Fetch the next digit (8) from the dividend, attach it to 104 and continue: 1048 / 513

Step 4:
513 goes into 1048 2 times with a remainder of 22.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
The remainder is 22 after subtracting 1026 from 1048.
Bring next digit (0) of the dividend behind the 22 and repeat the process: 220 / 513

Advancing to step 5:
220 divided by 513 is 0 with a remainder of 220.
Record the quotient 0 as the next digit in the result. 
Result so far: 120.0
If we take 0 away from 220, we end up with 220.
Bring next digit (4) of the dividend behind the 220 and repeat the process: 2204 / 513

On to step 6:
If we divide 2204 by 513, we get 4 and a remainder of 152.
The next digit of our result is 4. 
Result so far: 1204.0
Subtracting 2052 from 2204 leaves us with 152.
Include the next digit (3) from the dividend after 152, then repeat: 1523 / 513

On to step 7:
The number 513 fits into 1523 2 times, leaving a remainder of 497.
Put 2 as the next digit of the answer. 
Result so far: 12042.0
The remainder is 497 after subtracting 1026 from 1523.
Include the next digit (1) from the dividend after 497, then repeat: 4971 / 513

Going ahead to step 8:
If we divide 4971 by 513, we get 9 and a remainder of 354.
Record the quotient 9 as the next digit in the result. 
Result so far: 120429.0
If we subtract 4617 from 4971, we get 354.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3540, and continue the process.

On to step 9:
513 can be fit into 3540 6 times, resulting in a remainder of 462.
The number 6 becomes the next digit in our result. 
Result so far: 120429.6
The remainder is 462 after subtracting 3078 from 3540.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4620, and continue the process.

Moving on to step 10:
When dividing 4620 by 513, we get 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 120429.69
If we subtract 4617 from 4620, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 11:
513 can be fit into 30 0 times, resulting in a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 120429.69
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 12:
When dividing 300 by 513, we get 0 with a remainder of 300.
The next digit of our result is 0. 
Result so far: 120429.69
If we subtract 0 from 300, we get 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3000, and continue the process.

The final result is 120429.69 with a remainder of 0.003.