How do I find the factor combinations of the number 825,960?
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 825,960, 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 825,960.
Example:
1 x 825,960 = 825,960
and
-1 x -825,960 = 825,960
Notice both answers equal 825,960
With that explanation out of the way, let's continue. Next, we take the number 825,960 and divide it by 2:
825,960 ÷ 2 = 412,980
If the quotient is a whole number, then 2 and 412,980 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 825,960 by 3:
825,960 ÷ 3 = 275,320
If the quotient is a whole number, then 3 and 275,320 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:
825,960 ÷ 4 = 206,490
If the quotient is a whole number, then 4 and 206,490 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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