Q: What are the factor combinations of the number 21,311,213?

 A:
Positive:   1 x 213112137 x 304445911 x 193738359 x 36120777 x 276769413 x 51601649 x 328374543 x 4691
Negative: -1 x -21311213-7 x -3044459-11 x -1937383-59 x -361207-77 x -276769-413 x -51601-649 x -32837-4543 x -4691


How do I find the factor combinations of the number 21,311,213?

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 21,311,213, 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 21,311,213
-1 -21,311,213

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 21,311,213.

Example:
1 x 21,311,213 = 21,311,213
and
-1 x -21,311,213 = 21,311,213
Notice both answers equal 21,311,213

With that explanation out of the way, let's continue. Next, we take the number 21,311,213 and divide it by 2:

21,311,213 ÷ 2 = 10,655,606.5

If the quotient is a whole number, then 2 and 10,655,606.5 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 21,311,213
-1 -21,311,213

Now, we try dividing 21,311,213 by 3:

21,311,213 ÷ 3 = 7,103,737.6667

If the quotient is a whole number, then 3 and 7,103,737.6667 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 21,311,213
-1 -21,311,213

Let's try dividing by 4:

21,311,213 ÷ 4 = 5,327,803.25

If the quotient is a whole number, then 4 and 5,327,803.25 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 21,311,213
-1 21,311,213
Keep dividing by the next highest number until you cannot divide anymore.

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

171159774136494,5434,69132,83751,601276,769361,2071,937,3833,044,45921,311,213
-1-7-11-59-77-413-649-4,543-4,691-32,837-51,601-276,769-361,207-1,937,383-3,044,459-21,311,213

More Examples

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