Q: What are the factor combinations of the number 180,498?

 A:
Positive:   1 x 1804982 x 902493 x 601666 x 3008367 x 2694134 x 1347201 x 898402 x 449
Negative: -1 x -180498-2 x -90249-3 x -60166-6 x -30083-67 x -2694-134 x -1347-201 x -898-402 x -449


How do I find the factor combinations of the number 180,498?

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 180,498, 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.

1 180,498
-1 -180,498

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 180,498.

Example:
1 x 180,498 = 180,498
and
-1 x -180,498 = 180,498
Notice both answers equal 180,498

With that explanation out of the way, let's continue. Next, we take the number 180,498 and divide it by 2:

180,498 ÷ 2 = 90,249

If the quotient is a whole number, then 2 and 90,249 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 90,249 180,498
-1 -2 -90,249 -180,498

Now, we try dividing 180,498 by 3:

180,498 ÷ 3 = 60,166

If the quotient is a whole number, then 3 and 60,166 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 60,166 90,249 180,498
-1 -2 -3 -60,166 -90,249 -180,498

Let's try dividing by 4:

180,498 ÷ 4 = 45,124.5

If the quotient is a whole number, then 4 and 45,124.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 2 3 60,166 90,249 180,498
-1 -2 -3 -60,166 -90,249 180,498
Keep dividing by the next highest number until you cannot divide anymore.

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

1236671342014024498981,3472,69430,08360,16690,249180,498
-1-2-3-6-67-134-201-402-449-898-1,347-2,694-30,083-60,166-90,249-180,498

More Examples

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