How do I find the factor combinations of the number 857,534?
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 857,534, 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 857,534.
Example:
1 x 857,534 = 857,534
and
-1 x -857,534 = 857,534
Notice both answers equal 857,534
With that explanation out of the way, let's continue. Next, we take the number 857,534 and divide it by 2:
857,534 ÷ 2 = 428,767
If the quotient is a whole number, then 2 and 428,767 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 857,534 by 3:
857,534 ÷ 3 = 285,844.6667
If the quotient is a whole number, then 3 and 285,844.6667 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:
Let's try dividing by 4:
857,534 ÷ 4 = 214,383.5
If the quotient is a whole number, then 4 and 214,383.5 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:
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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