Q: What are the factor combinations of the number 23,569?

 A:
Positive:   1 x 235697 x 336713 x 181337 x 63749 x 48191 x 259
Negative: -1 x -23569-7 x -3367-13 x -1813-37 x -637-49 x -481-91 x -259


How do I find the factor combinations of the number 23,569?

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 23,569, 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 23,569
-1 -23,569

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 23,569.

Example:
1 x 23,569 = 23,569
and
-1 x -23,569 = 23,569
Notice both answers equal 23,569

With that explanation out of the way, let's continue. Next, we take the number 23,569 and divide it by 2:

23,569 ÷ 2 = 11,784.5

If the quotient is a whole number, then 2 and 11,784.5 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 23,569
-1 -23,569

Now, we try dividing 23,569 by 3:

23,569 ÷ 3 = 7,856.3333

If the quotient is a whole number, then 3 and 7,856.3333 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 23,569
-1 -23,569

Let's try dividing by 4:

23,569 ÷ 4 = 5,892.25

If the quotient is a whole number, then 4 and 5,892.25 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 23,569
-1 23,569
Keep dividing by the next highest number until you cannot divide anymore.

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

17133749912594816371,8133,36723,569
-1-7-13-37-49-91-259-481-637-1,813-3,367-23,569

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 23,569:


Ask a Question