Q: What are the factor combinations of the number 322,301,221?

 A:
Positive:   1 x 32230122111 x 2930011197 x 3322693379 x 850399797 x 4043931067 x 3020634169 x 773098767 x 36763
Negative: -1 x -322301221-11 x -29300111-97 x -3322693-379 x -850399-797 x -404393-1067 x -302063-4169 x -77309-8767 x -36763


How do I find the factor combinations of the number 322,301,221?

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 322,301,221, 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.

1 322,301,221
-1 -322,301,221

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 322,301,221.

Example:
1 x 322,301,221 = 322,301,221
and
-1 x -322,301,221 = 322,301,221
Notice both answers equal 322,301,221

With that explanation out of the way, let's continue. Next, we take the number 322,301,221 and divide it by 2:

322,301,221 ÷ 2 = 161,150,610.5

If the quotient is a whole number, then 2 and 161,150,610.5 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:

1 322,301,221
-1 -322,301,221

Now, we try dividing 322,301,221 by 3:

322,301,221 ÷ 3 = 107,433,740.3333

If the quotient is a whole number, then 3 and 107,433,740.3333 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:

1 322,301,221
-1 -322,301,221

Let's try dividing by 4:

322,301,221 ÷ 4 = 80,575,305.25

If the quotient is a whole number, then 4 and 80,575,305.25 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:

1 322,301,221
-1 322,301,221
Keep dividing by the next highest number until you cannot divide anymore.

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

111973797971,0674,1698,76736,76377,309302,063404,393850,3993,322,69329,300,111322,301,221
-1-11-97-379-797-1,067-4,169-8,767-36,763-77,309-302,063-404,393-850,399-3,322,693-29,300,111-322,301,221

More Examples

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