Q: What are the factor combinations of the number 23,407?

 A:
Positive:   1 x 2340789 x 263
Negative: -1 x -23407-89 x -263


How do I find the factor combinations of the number 23,407?

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 23,407, 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 23,407
-1 -23,407

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 23,407.

Example:
1 x 23,407 = 23,407
and
-1 x -23,407 = 23,407
Notice both answers equal 23,407

With that explanation out of the way, let's continue. Next, we take the number 23,407 and divide it by 2:

23,407 ÷ 2 = 11,703.5

If the quotient is a whole number, then 2 and 11,703.5 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 23,407
-1 -23,407

Now, we try dividing 23,407 by 3:

23,407 ÷ 3 = 7,802.3333

If the quotient is a whole number, then 3 and 7,802.3333 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 23,407
-1 -23,407

Let's try dividing by 4:

23,407 ÷ 4 = 5,851.75

If the quotient is a whole number, then 4 and 5,851.75 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 23,407
-1 23,407
Keep dividing by the next highest number until you cannot divide anymore.

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

18926323,407
-1-89-263-23,407

More Examples

Here are some more numbers to try:

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