Q: What are the factor combinations of the number 478,656,689?

 A:
Positive:   1 x 4786566897 x 68379527107 x 4473427149 x 3212461749 x 6390611043 x 4589234289 x 11160115943 x 30023
Negative: -1 x -478656689-7 x -68379527-107 x -4473427-149 x -3212461-749 x -639061-1043 x -458923-4289 x -111601-15943 x -30023


How do I find the factor combinations of the number 478,656,689?

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 478,656,689, 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.

1 478,656,689
-1 -478,656,689

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 478,656,689.

Example:
1 x 478,656,689 = 478,656,689
and
-1 x -478,656,689 = 478,656,689
Notice both answers equal 478,656,689

With that explanation out of the way, let's continue. Next, we take the number 478,656,689 and divide it by 2:

478,656,689 ÷ 2 = 239,328,344.5

If the quotient is a whole number, then 2 and 239,328,344.5 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:

1 478,656,689
-1 -478,656,689

Now, we try dividing 478,656,689 by 3:

478,656,689 ÷ 3 = 159,552,229.6667

If the quotient is a whole number, then 3 and 159,552,229.6667 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:

1 478,656,689
-1 -478,656,689

Let's try dividing by 4:

478,656,689 ÷ 4 = 119,664,172.25

If the quotient is a whole number, then 4 and 119,664,172.25 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:

1 478,656,689
-1 478,656,689
Keep dividing by the next highest number until you cannot divide anymore.

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

171071497491,0434,28915,94330,023111,601458,923639,0613,212,4614,473,42768,379,527478,656,689
-1-7-107-149-749-1,043-4,289-15,943-30,023-111,601-458,923-639,061-3,212,461-4,473,427-68,379,527-478,656,689

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