Q: What are the factor combinations of the number 413,404,663?

 A:
Positive:   1 x 4134046637 x 5905780937 x 11173099259 x 1596157809 x 5110071973 x 2095315663 x 7300113811 x 29933
Negative: -1 x -413404663-7 x -59057809-37 x -11173099-259 x -1596157-809 x -511007-1973 x -209531-5663 x -73001-13811 x -29933


How do I find the factor combinations of the number 413,404,663?

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 413,404,663, 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.

1 413,404,663
-1 -413,404,663

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 413,404,663.

Example:
1 x 413,404,663 = 413,404,663
and
-1 x -413,404,663 = 413,404,663
Notice both answers equal 413,404,663

With that explanation out of the way, let's continue. Next, we take the number 413,404,663 and divide it by 2:

413,404,663 ÷ 2 = 206,702,331.5

If the quotient is a whole number, then 2 and 206,702,331.5 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:

1 413,404,663
-1 -413,404,663

Now, we try dividing 413,404,663 by 3:

413,404,663 ÷ 3 = 137,801,554.3333

If the quotient is a whole number, then 3 and 137,801,554.3333 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:

1 413,404,663
-1 -413,404,663

Let's try dividing by 4:

413,404,663 ÷ 4 = 103,351,165.75

If the quotient is a whole number, then 4 and 103,351,165.75 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:

1 413,404,663
-1 413,404,663
Keep dividing by the next highest number until you cannot divide anymore.

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

17372598091,9735,66313,81129,93373,001209,531511,0071,596,15711,173,09959,057,809413,404,663
-1-7-37-259-809-1,973-5,663-13,811-29,933-73,001-209,531-511,007-1,596,157-11,173,099-59,057,809-413,404,663

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