Q: What are the factor combinations of the number 21,242,809?

 A:
Positive:   1 x 212428097 x 303468717 x 1249577119 x 178511137 x 155057959 x 221511303 x 163032329 x 9121
Negative: -1 x -21242809-7 x -3034687-17 x -1249577-119 x -178511-137 x -155057-959 x -22151-1303 x -16303-2329 x -9121


How do I find the factor combinations of the number 21,242,809?

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 21,242,809, 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 21,242,809
-1 -21,242,809

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 21,242,809.

Example:
1 x 21,242,809 = 21,242,809
and
-1 x -21,242,809 = 21,242,809
Notice both answers equal 21,242,809

With that explanation out of the way, let's continue. Next, we take the number 21,242,809 and divide it by 2:

21,242,809 ÷ 2 = 10,621,404.5

If the quotient is a whole number, then 2 and 10,621,404.5 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 21,242,809
-1 -21,242,809

Now, we try dividing 21,242,809 by 3:

21,242,809 ÷ 3 = 7,080,936.3333

If the quotient is a whole number, then 3 and 7,080,936.3333 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 21,242,809
-1 -21,242,809

Let's try dividing by 4:

21,242,809 ÷ 4 = 5,310,702.25

If the quotient is a whole number, then 4 and 5,310,702.25 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 21,242,809
-1 21,242,809
Keep dividing by the next highest number until you cannot divide anymore.

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

17171191379591,3032,3299,12116,30322,151155,057178,5111,249,5773,034,68721,242,809
-1-7-17-119-137-959-1,303-2,329-9,121-16,303-22,151-155,057-178,511-1,249,577-3,034,687-21,242,809

More Examples

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