Q: What are the factor combinations of the number 218,628?

 A:
Positive:   1 x 2186282 x 1093143 x 728764 x 546576 x 364389 x 2429212 x 1821918 x 1214636 x 6073
Negative: -1 x -218628-2 x -109314-3 x -72876-4 x -54657-6 x -36438-9 x -24292-12 x -18219-18 x -12146-36 x -6073


How do I find the factor combinations of the number 218,628?

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 218,628, 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.

1 218,628
-1 -218,628

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 218,628.

Example:
1 x 218,628 = 218,628
and
-1 x -218,628 = 218,628
Notice both answers equal 218,628

With that explanation out of the way, let's continue. Next, we take the number 218,628 and divide it by 2:

218,628 ÷ 2 = 109,314

If the quotient is a whole number, then 2 and 109,314 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 2 109,314 218,628
-1 -2 -109,314 -218,628

Now, we try dividing 218,628 by 3:

218,628 ÷ 3 = 72,876

If the quotient is a whole number, then 3 and 72,876 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 72,876 109,314 218,628
-1 -2 -3 -72,876 -109,314 -218,628

Let's try dividing by 4:

218,628 ÷ 4 = 54,657

If the quotient is a whole number, then 4 and 54,657 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 54,657 72,876 109,314 218,628
-1 -2 -3 -4 -54,657 -72,876 -109,314 218,628
Keep dividing by the next highest number until you cannot divide anymore.

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

1234691218366,07312,14618,21924,29236,43854,65772,876109,314218,628
-1-2-3-4-6-9-12-18-36-6,073-12,146-18,219-24,292-36,438-54,657-72,876-109,314-218,628

More Examples

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