How do I find the factor combinations of the number 225,072?
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 225,072, 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 225,072.
Example:
1 x 225,072 = 225,072
and
-1 x -225,072 = 225,072
Notice both answers equal 225,072
With that explanation out of the way, let's continue. Next, we take the number 225,072 and divide it by 2:
225,072 ÷ 2 = 112,536
If the quotient is a whole number, then 2 and 112,536 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 225,072 by 3:
225,072 ÷ 3 = 75,024
If the quotient is a whole number, then 3 and 75,024 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:
225,072 ÷ 4 = 56,268
If the quotient is a whole number, then 4 and 56,268 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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