Q: What are the factor combinations of the number 909,684?

 A:
Positive:   1 x 9096842 x 4548423 x 3032284 x 2274216 x 1516149 x 10107612 x 7580718 x 5053827 x 3369236 x 2526954 x 16846108 x 8423
Negative: -1 x -909684-2 x -454842-3 x -303228-4 x -227421-6 x -151614-9 x -101076-12 x -75807-18 x -50538-27 x -33692-36 x -25269-54 x -16846-108 x -8423


How do I find the factor combinations of the number 909,684?

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 909,684, 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.

1 909,684
-1 -909,684

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 909,684.

Example:
1 x 909,684 = 909,684
and
-1 x -909,684 = 909,684
Notice both answers equal 909,684

With that explanation out of the way, let's continue. Next, we take the number 909,684 and divide it by 2:

909,684 ÷ 2 = 454,842

If the quotient is a whole number, then 2 and 454,842 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 2 454,842 909,684
-1 -2 -454,842 -909,684

Now, we try dividing 909,684 by 3:

909,684 ÷ 3 = 303,228

If the quotient is a whole number, then 3 and 303,228 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 3 303,228 454,842 909,684
-1 -2 -3 -303,228 -454,842 -909,684

Let's try dividing by 4:

909,684 ÷ 4 = 227,421

If the quotient is a whole number, then 4 and 227,421 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 4 227,421 303,228 454,842 909,684
-1 -2 -3 -4 -227,421 -303,228 -454,842 909,684
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912182736541088,42316,84625,26933,69250,53875,807101,076151,614227,421303,228454,842909,684
-1-2-3-4-6-9-12-18-27-36-54-108-8,423-16,846-25,269-33,692-50,538-75,807-101,076-151,614-227,421-303,228-454,842-909,684

More Examples

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