Q: What are the factor combinations of the number 249,384?

 A:
Positive:   1 x 2493842 x 1246923 x 831284 x 623466 x 415648 x 3117312 x 2078224 x 10391
Negative: -1 x -249384-2 x -124692-3 x -83128-4 x -62346-6 x -41564-8 x -31173-12 x -20782-24 x -10391


How do I find the factor combinations of the number 249,384?

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 249,384, 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.

1 249,384
-1 -249,384

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 249,384.

Example:
1 x 249,384 = 249,384
and
-1 x -249,384 = 249,384
Notice both answers equal 249,384

With that explanation out of the way, let's continue. Next, we take the number 249,384 and divide it by 2:

249,384 ÷ 2 = 124,692

If the quotient is a whole number, then 2 and 124,692 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 2 124,692 249,384
-1 -2 -124,692 -249,384

Now, we try dividing 249,384 by 3:

249,384 ÷ 3 = 83,128

If the quotient is a whole number, then 3 and 83,128 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 83,128 124,692 249,384
-1 -2 -3 -83,128 -124,692 -249,384

Let's try dividing by 4:

249,384 ÷ 4 = 62,346

If the quotient is a whole number, then 4 and 62,346 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 62,346 83,128 124,692 249,384
-1 -2 -3 -4 -62,346 -83,128 -124,692 249,384
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122410,39120,78231,17341,56462,34683,128124,692249,384
-1-2-3-4-6-8-12-24-10,391-20,782-31,173-41,564-62,346-83,128-124,692-249,384

More Examples

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