Q: What are the factor combinations of the number 23,496,407?

 A:
Positive:   1 x 2349640711 x 213603719 x 123665361 x 38518797 x 242231209 x 112423361 x 65087671 x 350171067 x 220211159 x 202731843 x 127493971 x 5917
Negative: -1 x -23496407-11 x -2136037-19 x -1236653-61 x -385187-97 x -242231-209 x -112423-361 x -65087-671 x -35017-1067 x -22021-1159 x -20273-1843 x -12749-3971 x -5917


How do I find the factor combinations of the number 23,496,407?

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 23,496,407, 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 23,496,407
-1 -23,496,407

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 23,496,407.

Example:
1 x 23,496,407 = 23,496,407
and
-1 x -23,496,407 = 23,496,407
Notice both answers equal 23,496,407

With that explanation out of the way, let's continue. Next, we take the number 23,496,407 and divide it by 2:

23,496,407 ÷ 2 = 11,748,203.5

If the quotient is a whole number, then 2 and 11,748,203.5 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 23,496,407
-1 -23,496,407

Now, we try dividing 23,496,407 by 3:

23,496,407 ÷ 3 = 7,832,135.6667

If the quotient is a whole number, then 3 and 7,832,135.6667 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 23,496,407
-1 -23,496,407

Let's try dividing by 4:

23,496,407 ÷ 4 = 5,874,101.75

If the quotient is a whole number, then 4 and 5,874,101.75 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 23,496,407
-1 23,496,407
Keep dividing by the next highest number until you cannot divide anymore.

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

1111961972093616711,0671,1591,8433,9715,91712,74920,27322,02135,01765,087112,423242,231385,1871,236,6532,136,03723,496,407
-1-11-19-61-97-209-361-671-1,067-1,159-1,843-3,971-5,917-12,749-20,273-22,021-35,017-65,087-112,423-242,231-385,187-1,236,653-2,136,037-23,496,407

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