Q: What are the factor combinations of the number 89,623?

 A:
Positive:   1 x 8962319 x 471753 x 169189 x 1007
Negative: -1 x -89623-19 x -4717-53 x -1691-89 x -1007


How do I find the factor combinations of the number 89,623?

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 89,623, 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 89,623
-1 -89,623

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 89,623.

Example:
1 x 89,623 = 89,623
and
-1 x -89,623 = 89,623
Notice both answers equal 89,623

With that explanation out of the way, let's continue. Next, we take the number 89,623 and divide it by 2:

89,623 ÷ 2 = 44,811.5

If the quotient is a whole number, then 2 and 44,811.5 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 89,623
-1 -89,623

Now, we try dividing 89,623 by 3:

89,623 ÷ 3 = 29,874.3333

If the quotient is a whole number, then 3 and 29,874.3333 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 89,623
-1 -89,623

Let's try dividing by 4:

89,623 ÷ 4 = 22,405.75

If the quotient is a whole number, then 4 and 22,405.75 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 89,623
-1 89,623
Keep dividing by the next highest number until you cannot divide anymore.

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

11953891,0071,6914,71789,623
-1-19-53-89-1,007-1,691-4,717-89,623

More Examples

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