Q: What are the factor combinations of the number 362,184,893?

 A:
Positive:   1 x 3621848937 x 5174069959 x 6138727413 x 876961541 x 6694731621 x 2234333787 x 9563911347 x 31919
Negative: -1 x -362184893-7 x -51740699-59 x -6138727-413 x -876961-541 x -669473-1621 x -223433-3787 x -95639-11347 x -31919


How do I find the factor combinations of the number 362,184,893?

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 362,184,893, 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.

1 362,184,893
-1 -362,184,893

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 362,184,893.

Example:
1 x 362,184,893 = 362,184,893
and
-1 x -362,184,893 = 362,184,893
Notice both answers equal 362,184,893

With that explanation out of the way, let's continue. Next, we take the number 362,184,893 and divide it by 2:

362,184,893 ÷ 2 = 181,092,446.5

If the quotient is a whole number, then 2 and 181,092,446.5 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:

1 362,184,893
-1 -362,184,893

Now, we try dividing 362,184,893 by 3:

362,184,893 ÷ 3 = 120,728,297.6667

If the quotient is a whole number, then 3 and 120,728,297.6667 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:

1 362,184,893
-1 -362,184,893

Let's try dividing by 4:

362,184,893 ÷ 4 = 90,546,223.25

If the quotient is a whole number, then 4 and 90,546,223.25 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:

1 362,184,893
-1 362,184,893
Keep dividing by the next highest number until you cannot divide anymore.

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

17594135411,6213,78711,34731,91995,639223,433669,473876,9616,138,72751,740,699362,184,893
-1-7-59-413-541-1,621-3,787-11,347-31,919-95,639-223,433-669,473-876,961-6,138,727-51,740,699-362,184,893

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