Q: What are the factor combinations of the number 21,107,621?

 A:
Positive:   1 x 2110762129 x 72784931 x 68089153 x 398257443 x 47647899 x 234791537 x 137331643 x 12847
Negative: -1 x -21107621-29 x -727849-31 x -680891-53 x -398257-443 x -47647-899 x -23479-1537 x -13733-1643 x -12847


How do I find the factor combinations of the number 21,107,621?

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 21,107,621, 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 21,107,621
-1 -21,107,621

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 21,107,621.

Example:
1 x 21,107,621 = 21,107,621
and
-1 x -21,107,621 = 21,107,621
Notice both answers equal 21,107,621

With that explanation out of the way, let's continue. Next, we take the number 21,107,621 and divide it by 2:

21,107,621 ÷ 2 = 10,553,810.5

If the quotient is a whole number, then 2 and 10,553,810.5 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 21,107,621
-1 -21,107,621

Now, we try dividing 21,107,621 by 3:

21,107,621 ÷ 3 = 7,035,873.6667

If the quotient is a whole number, then 3 and 7,035,873.6667 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 21,107,621
-1 -21,107,621

Let's try dividing by 4:

21,107,621 ÷ 4 = 5,276,905.25

If the quotient is a whole number, then 4 and 5,276,905.25 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 21,107,621
-1 21,107,621
Keep dividing by the next highest number until you cannot divide anymore.

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

12931534438991,5371,64312,84713,73323,47947,647398,257680,891727,84921,107,621
-1-29-31-53-443-899-1,537-1,643-12,847-13,733-23,479-47,647-398,257-680,891-727,849-21,107,621

More Examples

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