Q: What are the factor combinations of the number 404,915?

 A:
Positive:   1 x 4049155 x 809837 x 5784523 x 1760535 x 11569115 x 3521161 x 2515503 x 805
Negative: -1 x -404915-5 x -80983-7 x -57845-23 x -17605-35 x -11569-115 x -3521-161 x -2515-503 x -805


How do I find the factor combinations of the number 404,915?

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 404,915, 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.

1 404,915
-1 -404,915

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 404,915.

Example:
1 x 404,915 = 404,915
and
-1 x -404,915 = 404,915
Notice both answers equal 404,915

With that explanation out of the way, let's continue. Next, we take the number 404,915 and divide it by 2:

404,915 ÷ 2 = 202,457.5

If the quotient is a whole number, then 2 and 202,457.5 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:

1 404,915
-1 -404,915

Now, we try dividing 404,915 by 3:

404,915 ÷ 3 = 134,971.6667

If the quotient is a whole number, then 3 and 134,971.6667 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:

1 404,915
-1 -404,915

Let's try dividing by 4:

404,915 ÷ 4 = 101,228.75

If the quotient is a whole number, then 4 and 101,228.75 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:

1 404,915
-1 404,915
Keep dividing by the next highest number until you cannot divide anymore.

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

15723351151615038052,5153,52111,56917,60557,84580,983404,915
-1-5-7-23-35-115-161-503-805-2,515-3,521-11,569-17,605-57,845-80,983-404,915

More Examples

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