Q: What are the factor combinations of the number 296,952?

 A:
Positive:   1 x 2969522 x 1484763 x 989844 x 742386 x 494928 x 3711912 x 2474624 x 12373
Negative: -1 x -296952-2 x -148476-3 x -98984-4 x -74238-6 x -49492-8 x -37119-12 x -24746-24 x -12373


How do I find the factor combinations of the number 296,952?

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 296,952, 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.

1 296,952
-1 -296,952

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 296,952.

Example:
1 x 296,952 = 296,952
and
-1 x -296,952 = 296,952
Notice both answers equal 296,952

With that explanation out of the way, let's continue. Next, we take the number 296,952 and divide it by 2:

296,952 ÷ 2 = 148,476

If the quotient is a whole number, then 2 and 148,476 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 2 148,476 296,952
-1 -2 -148,476 -296,952

Now, we try dividing 296,952 by 3:

296,952 ÷ 3 = 98,984

If the quotient is a whole number, then 3 and 98,984 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 98,984 148,476 296,952
-1 -2 -3 -98,984 -148,476 -296,952

Let's try dividing by 4:

296,952 ÷ 4 = 74,238

If the quotient is a whole number, then 4 and 74,238 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 74,238 98,984 148,476 296,952
-1 -2 -3 -4 -74,238 -98,984 -148,476 296,952
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122412,37324,74637,11949,49274,23898,984148,476296,952
-1-2-3-4-6-8-12-24-12,373-24,746-37,119-49,492-74,238-98,984-148,476-296,952

More Examples

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