Q: What are the factor combinations of the number 218,916?

 A:
Positive:   1 x 2189162 x 1094583 x 729724 x 547296 x 364869 x 2432412 x 1824318 x 1216227 x 810836 x 608154 x 4054108 x 2027
Negative: -1 x -218916-2 x -109458-3 x -72972-4 x -54729-6 x -36486-9 x -24324-12 x -18243-18 x -12162-27 x -8108-36 x -6081-54 x -4054-108 x -2027


How do I find the factor combinations of the number 218,916?

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 218,916, 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.

1 218,916
-1 -218,916

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 218,916.

Example:
1 x 218,916 = 218,916
and
-1 x -218,916 = 218,916
Notice both answers equal 218,916

With that explanation out of the way, let's continue. Next, we take the number 218,916 and divide it by 2:

218,916 ÷ 2 = 109,458

If the quotient is a whole number, then 2 and 109,458 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 2 109,458 218,916
-1 -2 -109,458 -218,916

Now, we try dividing 218,916 by 3:

218,916 ÷ 3 = 72,972

If the quotient is a whole number, then 3 and 72,972 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 72,972 109,458 218,916
-1 -2 -3 -72,972 -109,458 -218,916

Let's try dividing by 4:

218,916 ÷ 4 = 54,729

If the quotient is a whole number, then 4 and 54,729 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 54,729 72,972 109,458 218,916
-1 -2 -3 -4 -54,729 -72,972 -109,458 218,916
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912182736541082,0274,0546,0818,10812,16218,24324,32436,48654,72972,972109,458218,916
-1-2-3-4-6-9-12-18-27-36-54-108-2,027-4,054-6,081-8,108-12,162-18,243-24,324-36,486-54,729-72,972-109,458-218,916

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