Q: What are the factor combinations of the number 413,315?

 A:
Positive:   1 x 4133155 x 826637 x 5904535 x 1180949 x 8435241 x 1715245 x 1687343 x 1205
Negative: -1 x -413315-5 x -82663-7 x -59045-35 x -11809-49 x -8435-241 x -1715-245 x -1687-343 x -1205


How do I find the factor combinations of the number 413,315?

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 413,315, 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.

1 413,315
-1 -413,315

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 413,315.

Example:
1 x 413,315 = 413,315
and
-1 x -413,315 = 413,315
Notice both answers equal 413,315

With that explanation out of the way, let's continue. Next, we take the number 413,315 and divide it by 2:

413,315 ÷ 2 = 206,657.5

If the quotient is a whole number, then 2 and 206,657.5 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:

1 413,315
-1 -413,315

Now, we try dividing 413,315 by 3:

413,315 ÷ 3 = 137,771.6667

If the quotient is a whole number, then 3 and 137,771.6667 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:

1 413,315
-1 -413,315

Let's try dividing by 4:

413,315 ÷ 4 = 103,328.75

If the quotient is a whole number, then 4 and 103,328.75 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:

1 413,315
-1 413,315
Keep dividing by the next highest number until you cannot divide anymore.

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

15735492412453431,2051,6871,7158,43511,80959,04582,663413,315
-1-5-7-35-49-241-245-343-1,205-1,687-1,715-8,435-11,809-59,045-82,663-413,315

More Examples

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