Q: What are the factor combinations of the number 424,441?

 A:
Positive:   1 x 42444119 x 2233989 x 4769251 x 1691
Negative: -1 x -424441-19 x -22339-89 x -4769-251 x -1691


How do I find the factor combinations of the number 424,441?

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 424,441, 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.

1 424,441
-1 -424,441

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 424,441.

Example:
1 x 424,441 = 424,441
and
-1 x -424,441 = 424,441
Notice both answers equal 424,441

With that explanation out of the way, let's continue. Next, we take the number 424,441 and divide it by 2:

424,441 ÷ 2 = 212,220.5

If the quotient is a whole number, then 2 and 212,220.5 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:

1 424,441
-1 -424,441

Now, we try dividing 424,441 by 3:

424,441 ÷ 3 = 141,480.3333

If the quotient is a whole number, then 3 and 141,480.3333 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:

1 424,441
-1 -424,441

Let's try dividing by 4:

424,441 ÷ 4 = 106,110.25

If the quotient is a whole number, then 4 and 106,110.25 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:

1 424,441
-1 424,441
Keep dividing by the next highest number until you cannot divide anymore.

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

119892511,6914,76922,339424,441
-1-19-89-251-1,691-4,769-22,339-424,441

More Examples

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