How do I find the factor combinations of the number 413,805?
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 413,805, 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.
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 413,805.
Example:
1 x 413,805 = 413,805
and
-1 x -413,805 = 413,805
Notice both answers equal 413,805
With that explanation out of the way, let's continue. Next, we take the number 413,805 and divide it by 2:
413,805 ÷ 2 = 206,902.5
If the quotient is a whole number, then 2 and 206,902.5 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:
Now, we try dividing 413,805 by 3:
413,805 ÷ 3 = 137,935
If the quotient is a whole number, then 3 and 137,935 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:
Let's try dividing by 4:
413,805 ÷ 4 = 103,451.25
If the quotient is a whole number, then 4 and 103,451.25 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:
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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