Q: What are the factor combinations of the number 404,365?

 A:
Positive:   1 x 4043655 x 8087313 x 3110565 x 6221
Negative: -1 x -404365-5 x -80873-13 x -31105-65 x -6221


How do I find the factor combinations of the number 404,365?

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 404,365, 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.

1 404,365
-1 -404,365

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 404,365.

Example:
1 x 404,365 = 404,365
and
-1 x -404,365 = 404,365
Notice both answers equal 404,365

With that explanation out of the way, let's continue. Next, we take the number 404,365 and divide it by 2:

404,365 ÷ 2 = 202,182.5

If the quotient is a whole number, then 2 and 202,182.5 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:

1 404,365
-1 -404,365

Now, we try dividing 404,365 by 3:

404,365 ÷ 3 = 134,788.3333

If the quotient is a whole number, then 3 and 134,788.3333 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:

1 404,365
-1 -404,365

Let's try dividing by 4:

404,365 ÷ 4 = 101,091.25

If the quotient is a whole number, then 4 and 101,091.25 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:

1 404,365
-1 404,365
Keep dividing by the next highest number until you cannot divide anymore.

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

1513656,22131,10580,873404,365
-1-5-13-65-6,221-31,105-80,873-404,365

More Examples

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