Q: What are the factor combinations of the number 501,515,135?

 A:
Positive:   1 x 5015151355 x 10030302711 x 4559228555 x 91184572521 x 1989353617 x 13865512605 x 3978718085 x 27731
Negative: -1 x -501515135-5 x -100303027-11 x -45592285-55 x -9118457-2521 x -198935-3617 x -138655-12605 x -39787-18085 x -27731


How do I find the factor combinations of the number 501,515,135?

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 501,515,135, 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.

1 501,515,135
-1 -501,515,135

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 501,515,135.

Example:
1 x 501,515,135 = 501,515,135
and
-1 x -501,515,135 = 501,515,135
Notice both answers equal 501,515,135

With that explanation out of the way, let's continue. Next, we take the number 501,515,135 and divide it by 2:

501,515,135 ÷ 2 = 250,757,567.5

If the quotient is a whole number, then 2 and 250,757,567.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 501,515,135
-1 -501,515,135

Now, we try dividing 501,515,135 by 3:

501,515,135 ÷ 3 = 167,171,711.6667

If the quotient is a whole number, then 3 and 167,171,711.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 501,515,135
-1 -501,515,135

Let's try dividing by 4:

501,515,135 ÷ 4 = 125,378,783.75

If the quotient is a whole number, then 4 and 125,378,783.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 501,515,135
-1 501,515,135
Keep dividing by the next highest number until you cannot divide anymore.

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

1511552,5213,61712,60518,08527,73139,787138,655198,9359,118,45745,592,285100,303,027501,515,135
-1-5-11-55-2,521-3,617-12,605-18,085-27,731-39,787-138,655-198,935-9,118,457-45,592,285-100,303,027-501,515,135

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