Q: What are the factor combinations of the number 678,005?
A:
Positive:
1 x 6780055 x 135601
Negative:
-1 x -678005-5 x -135601
A:
Positive:
1 x 6780055 x 135601
Negative:
-1 x -678005-5 x -135601
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 678,005, it is easier to work with a table - it's called factoring from the outside in.
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.
1 | 678,005 | |
-1 | -678,005 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 678,005.
Example:
1 x 678,005 = 678,005
and
-1 x -678,005 = 678,005
Notice both answers equal 678,005
With that explanation out of the way, let's continue. Next, we take the number 678,005 and divide it by 2:
678,005 ÷ 2 = 339,002.5
If the quotient is a whole number, then 2 and 339,002.5 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:
1 | 678,005 | |
-1 | -678,005 |
Now, we try dividing 678,005 by 3:
678,005 ÷ 3 = 226,001.6667
If the quotient is a whole number, then 3 and 226,001.6667 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:
1 | 678,005 | |
-1 | -678,005 |
Let's try dividing by 4:
678,005 ÷ 4 = 169,501.25
If the quotient is a whole number, then 4 and 169,501.25 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:
1 | 678,005 | |
-1 | 678,005 |
If you did it right, you will end up with this table:
1 | 5 | 135,601 | 678,005 |
-1 | -5 | -135,601 | -678,005 |
Here are some more numbers to try:
Try the factor calculator