Q: What are the factor combinations of the number 12,413,023?

 A:
Positive:   1 x 124130237 x 177328919 x 65331749 x 25332767 x 185269133 x 93331199 x 62377469 x 26467931 x 133331273 x 97511393 x 89113283 x 3781
Negative: -1 x -12413023-7 x -1773289-19 x -653317-49 x -253327-67 x -185269-133 x -93331-199 x -62377-469 x -26467-931 x -13333-1273 x -9751-1393 x -8911-3283 x -3781


How do I find the factor combinations of the number 12,413,023?

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 12,413,023, 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 12,413,023
-1 -12,413,023

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 12,413,023.

Example:
1 x 12,413,023 = 12,413,023
and
-1 x -12,413,023 = 12,413,023
Notice both answers equal 12,413,023

With that explanation out of the way, let's continue. Next, we take the number 12,413,023 and divide it by 2:

12,413,023 ÷ 2 = 6,206,511.5

If the quotient is a whole number, then 2 and 6,206,511.5 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 12,413,023
-1 -12,413,023

Now, we try dividing 12,413,023 by 3:

12,413,023 ÷ 3 = 4,137,674.3333

If the quotient is a whole number, then 3 and 4,137,674.3333 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 12,413,023
-1 -12,413,023

Let's try dividing by 4:

12,413,023 ÷ 4 = 3,103,255.75

If the quotient is a whole number, then 4 and 3,103,255.75 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 12,413,023
-1 12,413,023
Keep dividing by the next highest number until you cannot divide anymore.

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

171949671331994699311,2731,3933,2833,7818,9119,75113,33326,46762,37793,331185,269253,327653,3171,773,28912,413,023
-1-7-19-49-67-133-199-469-931-1,273-1,393-3,283-3,781-8,911-9,751-13,333-26,467-62,377-93,331-185,269-253,327-653,317-1,773,289-12,413,023

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