How do I find the factor combinations of the number 624,504?
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 624,504, 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 624,504.
Example:
1 x 624,504 = 624,504
and
-1 x -624,504 = 624,504
Notice both answers equal 624,504
With that explanation out of the way, let's continue. Next, we take the number 624,504 and divide it by 2:
624,504 ÷ 2 = 312,252
If the quotient is a whole number, then 2 and 312,252 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 624,504 by 3:
624,504 ÷ 3 = 208,168
If the quotient is a whole number, then 3 and 208,168 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:
624,504 ÷ 4 = 156,126
If the quotient is a whole number, then 4 and 156,126 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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