Q: What are the factor combinations of the number 24,201,421?

 A:
Positive:   1 x 2420142117 x 142361319 x 127375931 x 780691323 x 74927527 x 45923589 x 410892417 x 10013
Negative: -1 x -24201421-17 x -1423613-19 x -1273759-31 x -780691-323 x -74927-527 x -45923-589 x -41089-2417 x -10013


How do I find the factor combinations of the number 24,201,421?

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 24,201,421, 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 24,201,421
-1 -24,201,421

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 24,201,421.

Example:
1 x 24,201,421 = 24,201,421
and
-1 x -24,201,421 = 24,201,421
Notice both answers equal 24,201,421

With that explanation out of the way, let's continue. Next, we take the number 24,201,421 and divide it by 2:

24,201,421 ÷ 2 = 12,100,710.5

If the quotient is a whole number, then 2 and 12,100,710.5 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 24,201,421
-1 -24,201,421

Now, we try dividing 24,201,421 by 3:

24,201,421 ÷ 3 = 8,067,140.3333

If the quotient is a whole number, then 3 and 8,067,140.3333 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 24,201,421
-1 -24,201,421

Let's try dividing by 4:

24,201,421 ÷ 4 = 6,050,355.25

If the quotient is a whole number, then 4 and 6,050,355.25 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 24,201,421
-1 24,201,421
Keep dividing by the next highest number until you cannot divide anymore.

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

11719313235275892,41710,01341,08945,92374,927780,6911,273,7591,423,61324,201,421
-1-17-19-31-323-527-589-2,417-10,013-41,089-45,923-74,927-780,691-1,273,759-1,423,613-24,201,421

More Examples

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