Q: What are the factor combinations of the number 21,342,413?

 A:
Positive:   1 x 2134241323 x 927931293 x 728413167 x 6739
Negative: -1 x -21342413-23 x -927931-293 x -72841-3167 x -6739


How do I find the factor combinations of the number 21,342,413?

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 21,342,413, 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 21,342,413
-1 -21,342,413

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 21,342,413.

Example:
1 x 21,342,413 = 21,342,413
and
-1 x -21,342,413 = 21,342,413
Notice both answers equal 21,342,413

With that explanation out of the way, let's continue. Next, we take the number 21,342,413 and divide it by 2:

21,342,413 ÷ 2 = 10,671,206.5

If the quotient is a whole number, then 2 and 10,671,206.5 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 21,342,413
-1 -21,342,413

Now, we try dividing 21,342,413 by 3:

21,342,413 ÷ 3 = 7,114,137.6667

If the quotient is a whole number, then 3 and 7,114,137.6667 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 21,342,413
-1 -21,342,413

Let's try dividing by 4:

21,342,413 ÷ 4 = 5,335,603.25

If the quotient is a whole number, then 4 and 5,335,603.25 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 21,342,413
-1 21,342,413
Keep dividing by the next highest number until you cannot divide anymore.

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

1232933,1676,73972,841927,93121,342,413
-1-23-293-3,167-6,739-72,841-927,931-21,342,413

More Examples

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