How do I find the factor combinations of the number 432,384?
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 432,384, 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.
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 432,384.
Example:
1 x 432,384 = 432,384
and
-1 x -432,384 = 432,384
Notice both answers equal 432,384
With that explanation out of the way, let's continue. Next, we take the number 432,384 and divide it by 2:
432,384 ÷ 2 = 216,192
If the quotient is a whole number, then 2 and 216,192 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:
Now, we try dividing 432,384 by 3:
432,384 ÷ 3 = 144,128
If the quotient is a whole number, then 3 and 144,128 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:
Let's try dividing by 4:
432,384 ÷ 4 = 108,096
If the quotient is a whole number, then 4 and 108,096 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:
Keep dividing by the next highest number until you cannot divide anymore.
If you did it right, you will end up with this table:
More Examples
Here are some more numbers to try:
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