Q: What are the factor combinations of the number 217,656?

 A:
Positive:   1 x 2176562 x 1088283 x 725524 x 544146 x 362768 x 272079 x 2418412 x 1813818 x 1209224 x 906936 x 604672 x 3023
Negative: -1 x -217656-2 x -108828-3 x -72552-4 x -54414-6 x -36276-8 x -27207-9 x -24184-12 x -18138-18 x -12092-24 x -9069-36 x -6046-72 x -3023


How do I find the factor combinations of the number 217,656?

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 217,656, 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.

1 217,656
-1 -217,656

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 217,656.

Example:
1 x 217,656 = 217,656
and
-1 x -217,656 = 217,656
Notice both answers equal 217,656

With that explanation out of the way, let's continue. Next, we take the number 217,656 and divide it by 2:

217,656 ÷ 2 = 108,828

If the quotient is a whole number, then 2 and 108,828 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 2 108,828 217,656
-1 -2 -108,828 -217,656

Now, we try dividing 217,656 by 3:

217,656 ÷ 3 = 72,552

If the quotient is a whole number, then 3 and 72,552 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 72,552 108,828 217,656
-1 -2 -3 -72,552 -108,828 -217,656

Let's try dividing by 4:

217,656 ÷ 4 = 54,414

If the quotient is a whole number, then 4 and 54,414 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 54,414 72,552 108,828 217,656
-1 -2 -3 -4 -54,414 -72,552 -108,828 217,656
Keep dividing by the next highest number until you cannot divide anymore.

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

123468912182436723,0236,0469,06912,09218,13824,18427,20736,27654,41472,552108,828217,656
-1-2-3-4-6-8-9-12-18-24-36-72-3,023-6,046-9,069-12,092-18,138-24,184-27,207-36,276-54,414-72,552-108,828-217,656

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