Q: What are the factor combinations of the number 12,398,921?

 A:
Positive:   1 x 1239892129 x 42754943 x 28834761 x 203261163 x 760671247 x 99431769 x 70092623 x 4727
Negative: -1 x -12398921-29 x -427549-43 x -288347-61 x -203261-163 x -76067-1247 x -9943-1769 x -7009-2623 x -4727


How do I find the factor combinations of the number 12,398,921?

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 12,398,921, 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 12,398,921
-1 -12,398,921

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 12,398,921.

Example:
1 x 12,398,921 = 12,398,921
and
-1 x -12,398,921 = 12,398,921
Notice both answers equal 12,398,921

With that explanation out of the way, let's continue. Next, we take the number 12,398,921 and divide it by 2:

12,398,921 ÷ 2 = 6,199,460.5

If the quotient is a whole number, then 2 and 6,199,460.5 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 12,398,921
-1 -12,398,921

Now, we try dividing 12,398,921 by 3:

12,398,921 ÷ 3 = 4,132,973.6667

If the quotient is a whole number, then 3 and 4,132,973.6667 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 12,398,921
-1 -12,398,921

Let's try dividing by 4:

12,398,921 ÷ 4 = 3,099,730.25

If the quotient is a whole number, then 4 and 3,099,730.25 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 12,398,921
-1 12,398,921
Keep dividing by the next highest number until you cannot divide anymore.

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

12943611631,2471,7692,6234,7277,0099,94376,067203,261288,347427,54912,398,921
-1-29-43-61-163-1,247-1,769-2,623-4,727-7,009-9,943-76,067-203,261-288,347-427,549-12,398,921

More Examples

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