Q: What are the factor combinations of the number 12,102,421?

 A:
Positive:   1 x 1210242141 x 295181229 x 528491289 x 9389
Negative: -1 x -12102421-41 x -295181-229 x -52849-1289 x -9389


How do I find the factor combinations of the number 12,102,421?

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 12,102,421, 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 12,102,421
-1 -12,102,421

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 12,102,421.

Example:
1 x 12,102,421 = 12,102,421
and
-1 x -12,102,421 = 12,102,421
Notice both answers equal 12,102,421

With that explanation out of the way, let's continue. Next, we take the number 12,102,421 and divide it by 2:

12,102,421 ÷ 2 = 6,051,210.5

If the quotient is a whole number, then 2 and 6,051,210.5 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 12,102,421
-1 -12,102,421

Now, we try dividing 12,102,421 by 3:

12,102,421 ÷ 3 = 4,034,140.3333

If the quotient is a whole number, then 3 and 4,034,140.3333 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 12,102,421
-1 -12,102,421

Let's try dividing by 4:

12,102,421 ÷ 4 = 3,025,605.25

If the quotient is a whole number, then 4 and 3,025,605.25 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 12,102,421
-1 12,102,421
Keep dividing by the next highest number until you cannot divide anymore.

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

1412291,2899,38952,849295,18112,102,421
-1-41-229-1,289-9,389-52,849-295,181-12,102,421

More Examples

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