Q: What are the factor combinations of the number 218,176,932?

 A:
Positive:   1 x 2181769322 x 1090884663 x 727256444 x 545442336 x 3636282212 x 18181411
Negative: -1 x -218176932-2 x -109088466-3 x -72725644-4 x -54544233-6 x -36362822-12 x -18181411


How do I find the factor combinations of the number 218,176,932?

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 218,176,932, 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.

1 218,176,932
-1 -218,176,932

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 218,176,932.

Example:
1 x 218,176,932 = 218,176,932
and
-1 x -218,176,932 = 218,176,932
Notice both answers equal 218,176,932

With that explanation out of the way, let's continue. Next, we take the number 218,176,932 and divide it by 2:

218,176,932 ÷ 2 = 109,088,466

If the quotient is a whole number, then 2 and 109,088,466 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 2 109,088,466 218,176,932
-1 -2 -109,088,466 -218,176,932

Now, we try dividing 218,176,932 by 3:

218,176,932 ÷ 3 = 72,725,644

If the quotient is a whole number, then 3 and 72,725,644 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 72,725,644 109,088,466 218,176,932
-1 -2 -3 -72,725,644 -109,088,466 -218,176,932

Let's try dividing by 4:

218,176,932 ÷ 4 = 54,544,233

If the quotient is a whole number, then 4 and 54,544,233 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 54,544,233 72,725,644 109,088,466 218,176,932
-1 -2 -3 -4 -54,544,233 -72,725,644 -109,088,466 218,176,932
Keep dividing by the next highest number until you cannot divide anymore.

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

123461218,181,41136,362,82254,544,23372,725,644109,088,466218,176,932
-1-2-3-4-6-12-18,181,411-36,362,822-54,544,233-72,725,644-109,088,466-218,176,932

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