Q: What are the factor combinations of the number 344,213,005?

 A:
Positive:   1 x 3442130055 x 6884260153 x 6494585265 x 1298917307 x 11212151535 x 2242434231 x 8135516271 x 21155
Negative: -1 x -344213005-5 x -68842601-53 x -6494585-265 x -1298917-307 x -1121215-1535 x -224243-4231 x -81355-16271 x -21155


How do I find the factor combinations of the number 344,213,005?

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 344,213,005, 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.

1 344,213,005
-1 -344,213,005

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 344,213,005.

Example:
1 x 344,213,005 = 344,213,005
and
-1 x -344,213,005 = 344,213,005
Notice both answers equal 344,213,005

With that explanation out of the way, let's continue. Next, we take the number 344,213,005 and divide it by 2:

344,213,005 ÷ 2 = 172,106,502.5

If the quotient is a whole number, then 2 and 172,106,502.5 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:

1 344,213,005
-1 -344,213,005

Now, we try dividing 344,213,005 by 3:

344,213,005 ÷ 3 = 114,737,668.3333

If the quotient is a whole number, then 3 and 114,737,668.3333 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:

1 344,213,005
-1 -344,213,005

Let's try dividing by 4:

344,213,005 ÷ 4 = 86,053,251.25

If the quotient is a whole number, then 4 and 86,053,251.25 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:

1 344,213,005
-1 344,213,005
Keep dividing by the next highest number until you cannot divide anymore.

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

15532653071,5354,23116,27121,15581,355224,2431,121,2151,298,9176,494,58568,842,601344,213,005
-1-5-53-265-307-1,535-4,231-16,271-21,155-81,355-224,243-1,121,215-1,298,917-6,494,585-68,842,601-344,213,005

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