Q: What are the factor combinations of the number 362,084,891?

 A:
Positive:   1 x 3620848917 x 5172641373 x 4960067167 x 2168173511 x 7085811169 x 3097394243 x 8533712191 x 29701
Negative: -1 x -362084891-7 x -51726413-73 x -4960067-167 x -2168173-511 x -708581-1169 x -309739-4243 x -85337-12191 x -29701


How do I find the factor combinations of the number 362,084,891?

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 362,084,891, 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.

1 362,084,891
-1 -362,084,891

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 362,084,891.

Example:
1 x 362,084,891 = 362,084,891
and
-1 x -362,084,891 = 362,084,891
Notice both answers equal 362,084,891

With that explanation out of the way, let's continue. Next, we take the number 362,084,891 and divide it by 2:

362,084,891 ÷ 2 = 181,042,445.5

If the quotient is a whole number, then 2 and 181,042,445.5 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:

1 362,084,891
-1 -362,084,891

Now, we try dividing 362,084,891 by 3:

362,084,891 ÷ 3 = 120,694,963.6667

If the quotient is a whole number, then 3 and 120,694,963.6667 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:

1 362,084,891
-1 -362,084,891

Let's try dividing by 4:

362,084,891 ÷ 4 = 90,521,222.75

If the quotient is a whole number, then 4 and 90,521,222.75 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:

1 362,084,891
-1 362,084,891
Keep dividing by the next highest number until you cannot divide anymore.

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

17731675111,1694,24312,19129,70185,337309,739708,5812,168,1734,960,06751,726,413362,084,891
-1-7-73-167-511-1,169-4,243-12,191-29,701-85,337-309,739-708,581-2,168,173-4,960,067-51,726,413-362,084,891

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