Q: What are the factor combinations of the number 21,013,025?

 A:
Positive:   1 x 210130255 x 420260511 x 191027525 x 84052143 x 48867555 x 382055215 x 97735275 x 76411473 x 444251075 x 195471777 x 118252365 x 8885
Negative: -1 x -21013025-5 x -4202605-11 x -1910275-25 x -840521-43 x -488675-55 x -382055-215 x -97735-275 x -76411-473 x -44425-1075 x -19547-1777 x -11825-2365 x -8885


How do I find the factor combinations of the number 21,013,025?

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 21,013,025, 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 21,013,025
-1 -21,013,025

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 21,013,025.

Example:
1 x 21,013,025 = 21,013,025
and
-1 x -21,013,025 = 21,013,025
Notice both answers equal 21,013,025

With that explanation out of the way, let's continue. Next, we take the number 21,013,025 and divide it by 2:

21,013,025 ÷ 2 = 10,506,512.5

If the quotient is a whole number, then 2 and 10,506,512.5 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 21,013,025
-1 -21,013,025

Now, we try dividing 21,013,025 by 3:

21,013,025 ÷ 3 = 7,004,341.6667

If the quotient is a whole number, then 3 and 7,004,341.6667 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 21,013,025
-1 -21,013,025

Let's try dividing by 4:

21,013,025 ÷ 4 = 5,253,256.25

If the quotient is a whole number, then 4 and 5,253,256.25 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 21,013,025
-1 21,013,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15112543552152754731,0751,7772,3658,88511,82519,54744,42576,41197,735382,055488,675840,5211,910,2754,202,60521,013,025
-1-5-11-25-43-55-215-275-473-1,075-1,777-2,365-8,885-11,825-19,547-44,425-76,411-97,735-382,055-488,675-840,521-1,910,275-4,202,605-21,013,025

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