Q: What are the factor combinations of the number 21,210,397?

 A:
Positive:   1 x 2121039713 x 163156929 x 731393127 x 167011377 x 56261443 x 478791651 x 128473683 x 5759
Negative: -1 x -21210397-13 x -1631569-29 x -731393-127 x -167011-377 x -56261-443 x -47879-1651 x -12847-3683 x -5759


How do I find the factor combinations of the number 21,210,397?

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 21,210,397, 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 21,210,397
-1 -21,210,397

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 21,210,397.

Example:
1 x 21,210,397 = 21,210,397
and
-1 x -21,210,397 = 21,210,397
Notice both answers equal 21,210,397

With that explanation out of the way, let's continue. Next, we take the number 21,210,397 and divide it by 2:

21,210,397 ÷ 2 = 10,605,198.5

If the quotient is a whole number, then 2 and 10,605,198.5 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 21,210,397
-1 -21,210,397

Now, we try dividing 21,210,397 by 3:

21,210,397 ÷ 3 = 7,070,132.3333

If the quotient is a whole number, then 3 and 7,070,132.3333 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 21,210,397
-1 -21,210,397

Let's try dividing by 4:

21,210,397 ÷ 4 = 5,302,599.25

If the quotient is a whole number, then 4 and 5,302,599.25 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 21,210,397
-1 21,210,397
Keep dividing by the next highest number until you cannot divide anymore.

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

113291273774431,6513,6835,75912,84747,87956,261167,011731,3931,631,56921,210,397
-1-13-29-127-377-443-1,651-3,683-5,759-12,847-47,879-56,261-167,011-731,393-1,631,569-21,210,397

More Examples

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