Q: What are the factor combinations of the number 282,180?

 A:
Positive:   1 x 2821802 x 1410903 x 940604 x 705455 x 564366 x 4703010 x 2821812 x 2351515 x 1881220 x 1410930 x 940660 x 4703
Negative: -1 x -282180-2 x -141090-3 x -94060-4 x -70545-5 x -56436-6 x -47030-10 x -28218-12 x -23515-15 x -18812-20 x -14109-30 x -9406-60 x -4703


How do I find the factor combinations of the number 282,180?

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 282,180, 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.

1 282,180
-1 -282,180

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 282,180.

Example:
1 x 282,180 = 282,180
and
-1 x -282,180 = 282,180
Notice both answers equal 282,180

With that explanation out of the way, let's continue. Next, we take the number 282,180 and divide it by 2:

282,180 ÷ 2 = 141,090

If the quotient is a whole number, then 2 and 141,090 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 2 141,090 282,180
-1 -2 -141,090 -282,180

Now, we try dividing 282,180 by 3:

282,180 ÷ 3 = 94,060

If the quotient is a whole number, then 3 and 94,060 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 94,060 141,090 282,180
-1 -2 -3 -94,060 -141,090 -282,180

Let's try dividing by 4:

282,180 ÷ 4 = 70,545

If the quotient is a whole number, then 4 and 70,545 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 70,545 94,060 141,090 282,180
-1 -2 -3 -4 -70,545 -94,060 -141,090 282,180
Keep dividing by the next highest number until you cannot divide anymore.

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

1234561012152030604,7039,40614,10918,81223,51528,21847,03056,43670,54594,060141,090282,180
-1-2-3-4-5-6-10-12-15-20-30-60-4,703-9,406-14,109-18,812-23,515-28,218-47,030-56,436-70,545-94,060-141,090-282,180

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