Q: What are the factor combinations of the number 12,502,259?

 A:
Positive:   1 x 125022597 x 178603711 x 113656917 x 73542777 x 162367119 x 105061187 x 668571309 x 9551
Negative: -1 x -12502259-7 x -1786037-11 x -1136569-17 x -735427-77 x -162367-119 x -105061-187 x -66857-1309 x -9551


How do I find the factor combinations of the number 12,502,259?

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 12,502,259, 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 12,502,259
-1 -12,502,259

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 12,502,259.

Example:
1 x 12,502,259 = 12,502,259
and
-1 x -12,502,259 = 12,502,259
Notice both answers equal 12,502,259

With that explanation out of the way, let's continue. Next, we take the number 12,502,259 and divide it by 2:

12,502,259 ÷ 2 = 6,251,129.5

If the quotient is a whole number, then 2 and 6,251,129.5 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 12,502,259
-1 -12,502,259

Now, we try dividing 12,502,259 by 3:

12,502,259 ÷ 3 = 4,167,419.6667

If the quotient is a whole number, then 3 and 4,167,419.6667 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 12,502,259
-1 -12,502,259

Let's try dividing by 4:

12,502,259 ÷ 4 = 3,125,564.75

If the quotient is a whole number, then 4 and 3,125,564.75 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 12,502,259
-1 12,502,259
Keep dividing by the next highest number until you cannot divide anymore.

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

171117771191871,3099,55166,857105,061162,367735,4271,136,5691,786,03712,502,259
-1-7-11-17-77-119-187-1,309-9,551-66,857-105,061-162,367-735,427-1,136,569-1,786,037-12,502,259

More Examples

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