Q: What are the factor combinations of the number 513,263,064?

 A:
Positive:   1 x 5132630642 x 2566315323 x 1710876884 x 1283157666 x 855438448 x 6415788312 x 4277192224 x 21385961
Negative: -1 x -513263064-2 x -256631532-3 x -171087688-4 x -128315766-6 x -85543844-8 x -64157883-12 x -42771922-24 x -21385961


How do I find the factor combinations of the number 513,263,064?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 513,263,064, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 513,263,064
-1 -513,263,064

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 513,263,064.

Example:
1 x 513,263,064 = 513,263,064
and
-1 x -513,263,064 = 513,263,064
Notice both answers equal 513,263,064

With that explanation out of the way, let's continue. Next, we take the number 513,263,064 and divide it by 2:

513,263,064 ÷ 2 = 256,631,532

If the quotient is a whole number, then 2 and 256,631,532 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 256,631,532 513,263,064
-1 -2 -256,631,532 -513,263,064

Now, we try dividing 513,263,064 by 3:

513,263,064 ÷ 3 = 171,087,688

If the quotient is a whole number, then 3 and 171,087,688 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 171,087,688 256,631,532 513,263,064
-1 -2 -3 -171,087,688 -256,631,532 -513,263,064

Let's try dividing by 4:

513,263,064 ÷ 4 = 128,315,766

If the quotient is a whole number, then 4 and 128,315,766 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 128,315,766 171,087,688 256,631,532 513,263,064
-1 -2 -3 -4 -128,315,766 -171,087,688 -256,631,532 513,263,064
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

123468122421,385,96142,771,92264,157,88385,543,844128,315,766171,087,688256,631,532513,263,064
-1-2-3-4-6-8-12-24-21,385,961-42,771,922-64,157,883-85,543,844-128,315,766-171,087,688-256,631,532-513,263,064

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