Q: What are the factor combinations of the number 443,805?

 A:
Positive:   1 x 4438053 x 1479355 x 8876115 x 29587
Negative: -1 x -443805-3 x -147935-5 x -88761-15 x -29587


How do I find the factor combinations of the number 443,805?

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 443,805, 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.

1 443,805
-1 -443,805

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 443,805.

Example:
1 x 443,805 = 443,805
and
-1 x -443,805 = 443,805
Notice both answers equal 443,805

With that explanation out of the way, let's continue. Next, we take the number 443,805 and divide it by 2:

443,805 ÷ 2 = 221,902.5

If the quotient is a whole number, then 2 and 221,902.5 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:

1 443,805
-1 -443,805

Now, we try dividing 443,805 by 3:

443,805 ÷ 3 = 147,935

If the quotient is a whole number, then 3 and 147,935 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 3 147,935 443,805
-1 -3 -147,935 -443,805

Let's try dividing by 4:

443,805 ÷ 4 = 110,951.25

If the quotient is a whole number, then 4 and 110,951.25 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 3 147,935 443,805
-1 -3 -147,935 443,805
Keep dividing by the next highest number until you cannot divide anymore.

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

1351529,58788,761147,935443,805
-1-3-5-15-29,587-88,761-147,935-443,805

More Examples

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