Q: What are the factor combinations of the number 21,920,717?

 A:
Positive:   1 x 219207177 x 313153113 x 168620991 x 240887139 x 157703973 x 225291733 x 126491807 x 12131
Negative: -1 x -21920717-7 x -3131531-13 x -1686209-91 x -240887-139 x -157703-973 x -22529-1733 x -12649-1807 x -12131


How do I find the factor combinations of the number 21,920,717?

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 21,920,717, 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 21,920,717
-1 -21,920,717

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 21,920,717.

Example:
1 x 21,920,717 = 21,920,717
and
-1 x -21,920,717 = 21,920,717
Notice both answers equal 21,920,717

With that explanation out of the way, let's continue. Next, we take the number 21,920,717 and divide it by 2:

21,920,717 ÷ 2 = 10,960,358.5

If the quotient is a whole number, then 2 and 10,960,358.5 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 21,920,717
-1 -21,920,717

Now, we try dividing 21,920,717 by 3:

21,920,717 ÷ 3 = 7,306,905.6667

If the quotient is a whole number, then 3 and 7,306,905.6667 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 21,920,717
-1 -21,920,717

Let's try dividing by 4:

21,920,717 ÷ 4 = 5,480,179.25

If the quotient is a whole number, then 4 and 5,480,179.25 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 21,920,717
-1 21,920,717
Keep dividing by the next highest number until you cannot divide anymore.

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

1713911399731,7331,80712,13112,64922,529157,703240,8871,686,2093,131,53121,920,717
-1-7-13-91-139-973-1,733-1,807-12,131-12,649-22,529-157,703-240,887-1,686,209-3,131,531-21,920,717

More Examples

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