Q: What are the factor combinations of the number 500,189?

 A:
Positive:   1 x 500189223 x 2243
Negative: -1 x -500189-223 x -2243


How do I find the factor combinations of the number 500,189?

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 500,189, 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.

1 500,189
-1 -500,189

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 500,189.

Example:
1 x 500,189 = 500,189
and
-1 x -500,189 = 500,189
Notice both answers equal 500,189

With that explanation out of the way, let's continue. Next, we take the number 500,189 and divide it by 2:

500,189 ÷ 2 = 250,094.5

If the quotient is a whole number, then 2 and 250,094.5 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:

1 500,189
-1 -500,189

Now, we try dividing 500,189 by 3:

500,189 ÷ 3 = 166,729.6667

If the quotient is a whole number, then 3 and 166,729.6667 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:

1 500,189
-1 -500,189

Let's try dividing by 4:

500,189 ÷ 4 = 125,047.25

If the quotient is a whole number, then 4 and 125,047.25 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:

1 500,189
-1 500,189
Keep dividing by the next highest number until you cannot divide anymore.

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

12232,243500,189
-1-223-2,243-500,189

More Examples

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