Q: What are the factor combinations of the number 40,032,005?

 A:
Positive:   1 x 400320055 x 800640113 x 307938531 x 129135565 x 615877155 x 258271403 x 993352015 x 19867
Negative: -1 x -40032005-5 x -8006401-13 x -3079385-31 x -1291355-65 x -615877-155 x -258271-403 x -99335-2015 x -19867


How do I find the factor combinations of the number 40,032,005?

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 40,032,005, 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 40,032,005
-1 -40,032,005

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 40,032,005.

Example:
1 x 40,032,005 = 40,032,005
and
-1 x -40,032,005 = 40,032,005
Notice both answers equal 40,032,005

With that explanation out of the way, let's continue. Next, we take the number 40,032,005 and divide it by 2:

40,032,005 ÷ 2 = 20,016,002.5

If the quotient is a whole number, then 2 and 20,016,002.5 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 40,032,005
-1 -40,032,005

Now, we try dividing 40,032,005 by 3:

40,032,005 ÷ 3 = 13,344,001.6667

If the quotient is a whole number, then 3 and 13,344,001.6667 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 40,032,005
-1 -40,032,005

Let's try dividing by 4:

40,032,005 ÷ 4 = 10,008,001.25

If the quotient is a whole number, then 4 and 10,008,001.25 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 40,032,005
-1 40,032,005
Keep dividing by the next highest number until you cannot divide anymore.

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

151331651554032,01519,86799,335258,271615,8771,291,3553,079,3858,006,40140,032,005
-1-5-13-31-65-155-403-2,015-19,867-99,335-258,271-615,877-1,291,355-3,079,385-8,006,401-40,032,005

More Examples

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