Q: What are the factor combinations of the number 322,011,024?

 A:
Positive:   1 x 3220110242 x 1610055123 x 1073370084 x 805027566 x 536685048 x 4025137812 x 2683425216 x 2012568924 x 1341712648 x 6708563
Negative: -1 x -322011024-2 x -161005512-3 x -107337008-4 x -80502756-6 x -53668504-8 x -40251378-12 x -26834252-16 x -20125689-24 x -13417126-48 x -6708563


How do I find the factor combinations of the number 322,011,024?

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 322,011,024, 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.

1 322,011,024
-1 -322,011,024

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 322,011,024.

Example:
1 x 322,011,024 = 322,011,024
and
-1 x -322,011,024 = 322,011,024
Notice both answers equal 322,011,024

With that explanation out of the way, let's continue. Next, we take the number 322,011,024 and divide it by 2:

322,011,024 ÷ 2 = 161,005,512

If the quotient is a whole number, then 2 and 161,005,512 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 2 161,005,512 322,011,024
-1 -2 -161,005,512 -322,011,024

Now, we try dividing 322,011,024 by 3:

322,011,024 ÷ 3 = 107,337,008

If the quotient is a whole number, then 3 and 107,337,008 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 3 107,337,008 161,005,512 322,011,024
-1 -2 -3 -107,337,008 -161,005,512 -322,011,024

Let's try dividing by 4:

322,011,024 ÷ 4 = 80,502,756

If the quotient is a whole number, then 4 and 80,502,756 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 80,502,756 107,337,008 161,005,512 322,011,024
-1 -2 -3 -4 -80,502,756 -107,337,008 -161,005,512 322,011,024
Keep dividing by the next highest number until you cannot divide anymore.

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

123468121624486,708,56313,417,12620,125,68926,834,25240,251,37853,668,50480,502,756107,337,008161,005,512322,011,024
-1-2-3-4-6-8-12-16-24-48-6,708,563-13,417,126-20,125,689-26,834,252-40,251,378-53,668,504-80,502,756-107,337,008-161,005,512-322,011,024

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