Q: What are the factor combinations of the number 23,120,005?

 A:
Positive:   1 x 231200055 x 462400137 x 62486547 x 491915185 x 124973235 x 983831739 x 132952659 x 8695
Negative: -1 x -23120005-5 x -4624001-37 x -624865-47 x -491915-185 x -124973-235 x -98383-1739 x -13295-2659 x -8695


How do I find the factor combinations of the number 23,120,005?

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 23,120,005, 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 23,120,005
-1 -23,120,005

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 23,120,005.

Example:
1 x 23,120,005 = 23,120,005
and
-1 x -23,120,005 = 23,120,005
Notice both answers equal 23,120,005

With that explanation out of the way, let's continue. Next, we take the number 23,120,005 and divide it by 2:

23,120,005 ÷ 2 = 11,560,002.5

If the quotient is a whole number, then 2 and 11,560,002.5 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 23,120,005
-1 -23,120,005

Now, we try dividing 23,120,005 by 3:

23,120,005 ÷ 3 = 7,706,668.3333

If the quotient is a whole number, then 3 and 7,706,668.3333 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 23,120,005
-1 -23,120,005

Let's try dividing by 4:

23,120,005 ÷ 4 = 5,780,001.25

If the quotient is a whole number, then 4 and 5,780,001.25 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 23,120,005
-1 23,120,005
Keep dividing by the next highest number until you cannot divide anymore.

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

1537471852351,7392,6598,69513,29598,383124,973491,915624,8654,624,00123,120,005
-1-5-37-47-185-235-1,739-2,659-8,695-13,295-98,383-124,973-491,915-624,865-4,624,001-23,120,005

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