Q: What are the factor combinations of the number 21,354,329?

 A:
Positive:   1 x 2135432917 x 1256137101 x 2114291717 x 12437
Negative: -1 x -21354329-17 x -1256137-101 x -211429-1717 x -12437


How do I find the factor combinations of the number 21,354,329?

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 21,354,329, 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 21,354,329
-1 -21,354,329

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 21,354,329.

Example:
1 x 21,354,329 = 21,354,329
and
-1 x -21,354,329 = 21,354,329
Notice both answers equal 21,354,329

With that explanation out of the way, let's continue. Next, we take the number 21,354,329 and divide it by 2:

21,354,329 ÷ 2 = 10,677,164.5

If the quotient is a whole number, then 2 and 10,677,164.5 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 21,354,329
-1 -21,354,329

Now, we try dividing 21,354,329 by 3:

21,354,329 ÷ 3 = 7,118,109.6667

If the quotient is a whole number, then 3 and 7,118,109.6667 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 21,354,329
-1 -21,354,329

Let's try dividing by 4:

21,354,329 ÷ 4 = 5,338,582.25

If the quotient is a whole number, then 4 and 5,338,582.25 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 21,354,329
-1 21,354,329
Keep dividing by the next highest number until you cannot divide anymore.

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

1171011,71712,437211,4291,256,13721,354,329
-1-17-101-1,717-12,437-211,429-1,256,137-21,354,329

More Examples

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