Q: What are the factor combinations of the number 23,515?

 A:
Positive:   1 x 235155 x 4703
Negative: -1 x -23515-5 x -4703


How do I find the factor combinations of the number 23,515?

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 23,515, 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 23,515
-1 -23,515

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 23,515.

Example:
1 x 23,515 = 23,515
and
-1 x -23,515 = 23,515
Notice both answers equal 23,515

With that explanation out of the way, let's continue. Next, we take the number 23,515 and divide it by 2:

23,515 ÷ 2 = 11,757.5

If the quotient is a whole number, then 2 and 11,757.5 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 23,515
-1 -23,515

Now, we try dividing 23,515 by 3:

23,515 ÷ 3 = 7,838.3333

If the quotient is a whole number, then 3 and 7,838.3333 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 23,515
-1 -23,515

Let's try dividing by 4:

23,515 ÷ 4 = 5,878.75

If the quotient is a whole number, then 4 and 5,878.75 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 23,515
-1 23,515
Keep dividing by the next highest number until you cannot divide anymore.

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

154,70323,515
-1-5-4,703-23,515

More Examples

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