Q: What are the factor combinations of the number 237,924?

 A:
Positive:   1 x 2379242 x 1189623 x 793084 x 594816 x 396549 x 2643612 x 1982718 x 1321827 x 881236 x 660954 x 4406108 x 2203
Negative: -1 x -237924-2 x -118962-3 x -79308-4 x -59481-6 x -39654-9 x -26436-12 x -19827-18 x -13218-27 x -8812-36 x -6609-54 x -4406-108 x -2203


How do I find the factor combinations of the number 237,924?

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 237,924, 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.

1 237,924
-1 -237,924

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 237,924.

Example:
1 x 237,924 = 237,924
and
-1 x -237,924 = 237,924
Notice both answers equal 237,924

With that explanation out of the way, let's continue. Next, we take the number 237,924 and divide it by 2:

237,924 ÷ 2 = 118,962

If the quotient is a whole number, then 2 and 118,962 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 2 118,962 237,924
-1 -2 -118,962 -237,924

Now, we try dividing 237,924 by 3:

237,924 ÷ 3 = 79,308

If the quotient is a whole number, then 3 and 79,308 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 79,308 118,962 237,924
-1 -2 -3 -79,308 -118,962 -237,924

Let's try dividing by 4:

237,924 ÷ 4 = 59,481

If the quotient is a whole number, then 4 and 59,481 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 59,481 79,308 118,962 237,924
-1 -2 -3 -4 -59,481 -79,308 -118,962 237,924
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912182736541082,2034,4066,6098,81213,21819,82726,43639,65459,48179,308118,962237,924
-1-2-3-4-6-9-12-18-27-36-54-108-2,203-4,406-6,609-8,812-13,218-19,827-26,436-39,654-59,481-79,308-118,962-237,924

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