Q: What are the factor combinations of the number 21,450,421?

 A:
Positive:   1 x 2145042123 x 93262741 x 52318143 x 498847529 x 40549943 x 22747989 x 216891763 x 12167
Negative: -1 x -21450421-23 x -932627-41 x -523181-43 x -498847-529 x -40549-943 x -22747-989 x -21689-1763 x -12167


How do I find the factor combinations of the number 21,450,421?

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 21,450,421, 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 21,450,421
-1 -21,450,421

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 21,450,421.

Example:
1 x 21,450,421 = 21,450,421
and
-1 x -21,450,421 = 21,450,421
Notice both answers equal 21,450,421

With that explanation out of the way, let's continue. Next, we take the number 21,450,421 and divide it by 2:

21,450,421 ÷ 2 = 10,725,210.5

If the quotient is a whole number, then 2 and 10,725,210.5 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 21,450,421
-1 -21,450,421

Now, we try dividing 21,450,421 by 3:

21,450,421 ÷ 3 = 7,150,140.3333

If the quotient is a whole number, then 3 and 7,150,140.3333 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 21,450,421
-1 -21,450,421

Let's try dividing by 4:

21,450,421 ÷ 4 = 5,362,605.25

If the quotient is a whole number, then 4 and 5,362,605.25 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 21,450,421
-1 21,450,421
Keep dividing by the next highest number until you cannot divide anymore.

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

12341435299439891,76312,16721,68922,74740,549498,847523,181932,62721,450,421
-1-23-41-43-529-943-989-1,763-12,167-21,689-22,747-40,549-498,847-523,181-932,627-21,450,421

More Examples

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