Q: What are the factor combinations of the number 22,421,021?

 A:
Positive:   1 x 224210217 x 320300323 x 97482747 x 477043161 x 139261329 x 681491081 x 207412963 x 7567
Negative: -1 x -22421021-7 x -3203003-23 x -974827-47 x -477043-161 x -139261-329 x -68149-1081 x -20741-2963 x -7567


How do I find the factor combinations of the number 22,421,021?

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 22,421,021, 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 22,421,021
-1 -22,421,021

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 22,421,021.

Example:
1 x 22,421,021 = 22,421,021
and
-1 x -22,421,021 = 22,421,021
Notice both answers equal 22,421,021

With that explanation out of the way, let's continue. Next, we take the number 22,421,021 and divide it by 2:

22,421,021 ÷ 2 = 11,210,510.5

If the quotient is a whole number, then 2 and 11,210,510.5 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 22,421,021
-1 -22,421,021

Now, we try dividing 22,421,021 by 3:

22,421,021 ÷ 3 = 7,473,673.6667

If the quotient is a whole number, then 3 and 7,473,673.6667 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 22,421,021
-1 -22,421,021

Let's try dividing by 4:

22,421,021 ÷ 4 = 5,605,255.25

If the quotient is a whole number, then 4 and 5,605,255.25 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 22,421,021
-1 22,421,021
Keep dividing by the next highest number until you cannot divide anymore.

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

1723471613291,0812,9637,56720,74168,149139,261477,043974,8273,203,00322,421,021
-1-7-23-47-161-329-1,081-2,963-7,567-20,741-68,149-139,261-477,043-974,827-3,203,003-22,421,021

More Examples

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