Q: What are the factor combinations of the number 123,889,823?

 A:
Positive:   1 x 12388982319 x 652051741 x 3021703359 x 345097443 x 279661779 x 1590376821 x 181638417 x 14719
Negative: -1 x -123889823-19 x -6520517-41 x -3021703-359 x -345097-443 x -279661-779 x -159037-6821 x -18163-8417 x -14719


How do I find the factor combinations of the number 123,889,823?

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 123,889,823, 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.

1 123,889,823
-1 -123,889,823

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 123,889,823.

Example:
1 x 123,889,823 = 123,889,823
and
-1 x -123,889,823 = 123,889,823
Notice both answers equal 123,889,823

With that explanation out of the way, let's continue. Next, we take the number 123,889,823 and divide it by 2:

123,889,823 ÷ 2 = 61,944,911.5

If the quotient is a whole number, then 2 and 61,944,911.5 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:

1 123,889,823
-1 -123,889,823

Now, we try dividing 123,889,823 by 3:

123,889,823 ÷ 3 = 41,296,607.6667

If the quotient is a whole number, then 3 and 41,296,607.6667 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:

1 123,889,823
-1 -123,889,823

Let's try dividing by 4:

123,889,823 ÷ 4 = 30,972,455.75

If the quotient is a whole number, then 4 and 30,972,455.75 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:

1 123,889,823
-1 123,889,823
Keep dividing by the next highest number until you cannot divide anymore.

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

119413594437796,8218,41714,71918,163159,037279,661345,0973,021,7036,520,517123,889,823
-1-19-41-359-443-779-6,821-8,417-14,719-18,163-159,037-279,661-345,097-3,021,703-6,520,517-123,889,823

More Examples

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