Q: What are the factor combinations of the number 413,015?

 A:
Positive:   1 x 4130155 x 8260317 x 2429543 x 960585 x 4859113 x 3655215 x 1921565 x 731
Negative: -1 x -413015-5 x -82603-17 x -24295-43 x -9605-85 x -4859-113 x -3655-215 x -1921-565 x -731


How do I find the factor combinations of the number 413,015?

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 413,015, 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.

1 413,015
-1 -413,015

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 413,015.

Example:
1 x 413,015 = 413,015
and
-1 x -413,015 = 413,015
Notice both answers equal 413,015

With that explanation out of the way, let's continue. Next, we take the number 413,015 and divide it by 2:

413,015 ÷ 2 = 206,507.5

If the quotient is a whole number, then 2 and 206,507.5 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:

1 413,015
-1 -413,015

Now, we try dividing 413,015 by 3:

413,015 ÷ 3 = 137,671.6667

If the quotient is a whole number, then 3 and 137,671.6667 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:

1 413,015
-1 -413,015

Let's try dividing by 4:

413,015 ÷ 4 = 103,253.75

If the quotient is a whole number, then 4 and 103,253.75 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:

1 413,015
-1 413,015
Keep dividing by the next highest number until you cannot divide anymore.

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

151743851132155657311,9213,6554,8599,60524,29582,603413,015
-1-5-17-43-85-113-215-565-731-1,921-3,655-4,859-9,605-24,295-82,603-413,015

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