Q: What are the factor combinations of the number 21,531,389?

 A:
Positive:   1 x 2153138911 x 195739919 x 113323171 x 303259209 x 103021781 x 275691349 x 159611451 x 14839
Negative: -1 x -21531389-11 x -1957399-19 x -1133231-71 x -303259-209 x -103021-781 x -27569-1349 x -15961-1451 x -14839


How do I find the factor combinations of the number 21,531,389?

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 21,531,389, 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 21,531,389
-1 -21,531,389

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 21,531,389.

Example:
1 x 21,531,389 = 21,531,389
and
-1 x -21,531,389 = 21,531,389
Notice both answers equal 21,531,389

With that explanation out of the way, let's continue. Next, we take the number 21,531,389 and divide it by 2:

21,531,389 ÷ 2 = 10,765,694.5

If the quotient is a whole number, then 2 and 10,765,694.5 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 21,531,389
-1 -21,531,389

Now, we try dividing 21,531,389 by 3:

21,531,389 ÷ 3 = 7,177,129.6667

If the quotient is a whole number, then 3 and 7,177,129.6667 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 21,531,389
-1 -21,531,389

Let's try dividing by 4:

21,531,389 ÷ 4 = 5,382,847.25

If the quotient is a whole number, then 4 and 5,382,847.25 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 21,531,389
-1 21,531,389
Keep dividing by the next highest number until you cannot divide anymore.

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

11119712097811,3491,45114,83915,96127,569103,021303,2591,133,2311,957,39921,531,389
-1-11-19-71-209-781-1,349-1,451-14,839-15,961-27,569-103,021-303,259-1,133,231-1,957,399-21,531,389

More Examples

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