Q: What are the factor combinations of the number 215,892?

 A:
Positive:   1 x 2158922 x 1079463 x 719644 x 539736 x 359829 x 2398812 x 1799118 x 1199427 x 799636 x 599754 x 3998108 x 1999
Negative: -1 x -215892-2 x -107946-3 x -71964-4 x -53973-6 x -35982-9 x -23988-12 x -17991-18 x -11994-27 x -7996-36 x -5997-54 x -3998-108 x -1999


How do I find the factor combinations of the number 215,892?

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 215,892, 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.

1 215,892
-1 -215,892

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 215,892.

Example:
1 x 215,892 = 215,892
and
-1 x -215,892 = 215,892
Notice both answers equal 215,892

With that explanation out of the way, let's continue. Next, we take the number 215,892 and divide it by 2:

215,892 ÷ 2 = 107,946

If the quotient is a whole number, then 2 and 107,946 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 2 107,946 215,892
-1 -2 -107,946 -215,892

Now, we try dividing 215,892 by 3:

215,892 ÷ 3 = 71,964

If the quotient is a whole number, then 3 and 71,964 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 71,964 107,946 215,892
-1 -2 -3 -71,964 -107,946 -215,892

Let's try dividing by 4:

215,892 ÷ 4 = 53,973

If the quotient is a whole number, then 4 and 53,973 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 53,973 71,964 107,946 215,892
-1 -2 -3 -4 -53,973 -71,964 -107,946 215,892
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912182736541081,9993,9985,9977,99611,99417,99123,98835,98253,97371,964107,946215,892
-1-2-3-4-6-9-12-18-27-36-54-108-1,999-3,998-5,997-7,996-11,994-17,991-23,988-35,982-53,973-71,964-107,946-215,892

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