Q: What are the factor combinations of the number 21,464,735?

 A:
Positive:   1 x 214647355 x 429294753 x 404995107 x 200605265 x 80999535 x 40121757 x 283553785 x 5671
Negative: -1 x -21464735-5 x -4292947-53 x -404995-107 x -200605-265 x -80999-535 x -40121-757 x -28355-3785 x -5671


How do I find the factor combinations of the number 21,464,735?

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 21,464,735, 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 21,464,735
-1 -21,464,735

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 21,464,735.

Example:
1 x 21,464,735 = 21,464,735
and
-1 x -21,464,735 = 21,464,735
Notice both answers equal 21,464,735

With that explanation out of the way, let's continue. Next, we take the number 21,464,735 and divide it by 2:

21,464,735 ÷ 2 = 10,732,367.5

If the quotient is a whole number, then 2 and 10,732,367.5 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 21,464,735
-1 -21,464,735

Now, we try dividing 21,464,735 by 3:

21,464,735 ÷ 3 = 7,154,911.6667

If the quotient is a whole number, then 3 and 7,154,911.6667 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 21,464,735
-1 -21,464,735

Let's try dividing by 4:

21,464,735 ÷ 4 = 5,366,183.75

If the quotient is a whole number, then 4 and 5,366,183.75 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 21,464,735
-1 21,464,735
Keep dividing by the next highest number until you cannot divide anymore.

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

15531072655357573,7855,67128,35540,12180,999200,605404,9954,292,94721,464,735
-1-5-53-107-265-535-757-3,785-5,671-28,355-40,121-80,999-200,605-404,995-4,292,947-21,464,735

More Examples

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