Q: What are the factor combinations of the number 263,916?

 A:
Positive:   1 x 2639162 x 1319583 x 879724 x 659796 x 439869 x 2932412 x 2199318 x 1466236 x 7331
Negative: -1 x -263916-2 x -131958-3 x -87972-4 x -65979-6 x -43986-9 x -29324-12 x -21993-18 x -14662-36 x -7331


How do I find the factor combinations of the number 263,916?

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 263,916, 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.

1 263,916
-1 -263,916

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 263,916.

Example:
1 x 263,916 = 263,916
and
-1 x -263,916 = 263,916
Notice both answers equal 263,916

With that explanation out of the way, let's continue. Next, we take the number 263,916 and divide it by 2:

263,916 ÷ 2 = 131,958

If the quotient is a whole number, then 2 and 131,958 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 131,958 263,916
-1 -2 -131,958 -263,916

Now, we try dividing 263,916 by 3:

263,916 ÷ 3 = 87,972

If the quotient is a whole number, then 3 and 87,972 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 87,972 131,958 263,916
-1 -2 -3 -87,972 -131,958 -263,916

Let's try dividing by 4:

263,916 ÷ 4 = 65,979

If the quotient is a whole number, then 4 and 65,979 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 65,979 87,972 131,958 263,916
-1 -2 -3 -4 -65,979 -87,972 -131,958 263,916
Keep dividing by the next highest number until you cannot divide anymore.

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

1234691218367,33114,66221,99329,32443,98665,97987,972131,958263,916
-1-2-3-4-6-9-12-18-36-7,331-14,662-21,993-29,324-43,986-65,979-87,972-131,958-263,916

More Examples

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