Q: What are the factor combinations of the number 28,189?

 A:
Positive:   1 x 281897 x 4027
Negative: -1 x -28189-7 x -4027


How do I find the factor combinations of the number 28,189?

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 28,189, 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 28,189
-1 -28,189

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 28,189.

Example:
1 x 28,189 = 28,189
and
-1 x -28,189 = 28,189
Notice both answers equal 28,189

With that explanation out of the way, let's continue. Next, we take the number 28,189 and divide it by 2:

28,189 ÷ 2 = 14,094.5

If the quotient is a whole number, then 2 and 14,094.5 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 28,189
-1 -28,189

Now, we try dividing 28,189 by 3:

28,189 ÷ 3 = 9,396.3333

If the quotient is a whole number, then 3 and 9,396.3333 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 28,189
-1 -28,189

Let's try dividing by 4:

28,189 ÷ 4 = 7,047.25

If the quotient is a whole number, then 4 and 7,047.25 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 28,189
-1 28,189
Keep dividing by the next highest number until you cannot divide anymore.

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

174,02728,189
-1-7-4,027-28,189

More Examples

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