Q: What are the factor combinations of the number 238,876?

 A:
Positive:   1 x 2388762 x 1194384 x 5971911 x 2171622 x 1085844 x 542961 x 391689 x 2684122 x 1958178 x 1342244 x 979356 x 671
Negative: -1 x -238876-2 x -119438-4 x -59719-11 x -21716-22 x -10858-44 x -5429-61 x -3916-89 x -2684-122 x -1958-178 x -1342-244 x -979-356 x -671


How do I find the factor combinations of the number 238,876?

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 238,876, 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.

1 238,876
-1 -238,876

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 238,876.

Example:
1 x 238,876 = 238,876
and
-1 x -238,876 = 238,876
Notice both answers equal 238,876

With that explanation out of the way, let's continue. Next, we take the number 238,876 and divide it by 2:

238,876 ÷ 2 = 119,438

If the quotient is a whole number, then 2 and 119,438 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 2 119,438 238,876
-1 -2 -119,438 -238,876

Now, we try dividing 238,876 by 3:

238,876 ÷ 3 = 79,625.3333

If the quotient is a whole number, then 3 and 79,625.3333 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 2 119,438 238,876
-1 -2 -119,438 -238,876

Let's try dividing by 4:

238,876 ÷ 4 = 59,719

If the quotient is a whole number, then 4 and 59,719 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 4 59,719 119,438 238,876
-1 -2 -4 -59,719 -119,438 238,876
Keep dividing by the next highest number until you cannot divide anymore.

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

12411224461891221782443566719791,3421,9582,6843,9165,42910,85821,71659,719119,438238,876
-1-2-4-11-22-44-61-89-122-178-244-356-671-979-1,342-1,958-2,684-3,916-5,429-10,858-21,716-59,719-119,438-238,876

More Examples

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