Q: What are the factor combinations of the number 301,442,005?

 A:
Positive:   1 x 3014420055 x 6028840153 x 5687585107 x 2817215265 x 1137517535 x 5634435671 x 5315510631 x 28355
Negative: -1 x -301442005-5 x -60288401-53 x -5687585-107 x -2817215-265 x -1137517-535 x -563443-5671 x -53155-10631 x -28355


How do I find the factor combinations of the number 301,442,005?

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 301,442,005, 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.

1 301,442,005
-1 -301,442,005

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 301,442,005.

Example:
1 x 301,442,005 = 301,442,005
and
-1 x -301,442,005 = 301,442,005
Notice both answers equal 301,442,005

With that explanation out of the way, let's continue. Next, we take the number 301,442,005 and divide it by 2:

301,442,005 ÷ 2 = 150,721,002.5

If the quotient is a whole number, then 2 and 150,721,002.5 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:

1 301,442,005
-1 -301,442,005

Now, we try dividing 301,442,005 by 3:

301,442,005 ÷ 3 = 100,480,668.3333

If the quotient is a whole number, then 3 and 100,480,668.3333 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:

1 301,442,005
-1 -301,442,005

Let's try dividing by 4:

301,442,005 ÷ 4 = 75,360,501.25

If the quotient is a whole number, then 4 and 75,360,501.25 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:

1 301,442,005
-1 301,442,005
Keep dividing by the next highest number until you cannot divide anymore.

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

15531072655355,67110,63128,35553,155563,4431,137,5172,817,2155,687,58560,288,401301,442,005
-1-5-53-107-265-535-5,671-10,631-28,355-53,155-563,443-1,137,517-2,817,215-5,687,585-60,288,401-301,442,005

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