Q: What are the factor combinations of the number 407,915?

 A:
Positive:   1 x 4079155 x 8158317 x 2399585 x 4799
Negative: -1 x -407915-5 x -81583-17 x -23995-85 x -4799


How do I find the factor combinations of the number 407,915?

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 407,915, 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.

1 407,915
-1 -407,915

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 407,915.

Example:
1 x 407,915 = 407,915
and
-1 x -407,915 = 407,915
Notice both answers equal 407,915

With that explanation out of the way, let's continue. Next, we take the number 407,915 and divide it by 2:

407,915 ÷ 2 = 203,957.5

If the quotient is a whole number, then 2 and 203,957.5 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:

1 407,915
-1 -407,915

Now, we try dividing 407,915 by 3:

407,915 ÷ 3 = 135,971.6667

If the quotient is a whole number, then 3 and 135,971.6667 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:

1 407,915
-1 -407,915

Let's try dividing by 4:

407,915 ÷ 4 = 101,978.75

If the quotient is a whole number, then 4 and 101,978.75 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:

1 407,915
-1 407,915
Keep dividing by the next highest number until you cannot divide anymore.

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

1517854,79923,99581,583407,915
-1-5-17-85-4,799-23,995-81,583-407,915

More Examples

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