Q: What are the factor combinations of the number 407,021?
A:
Positive:
1 x 407021191 x 2131
Negative:
-1 x -407021-191 x -2131
A:
Positive:
1 x 407021191 x 2131
Negative:
-1 x -407021-191 x -2131
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 407,021, 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 | 407,021 | |
-1 | -407,021 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 407,021.
Example:
1 x 407,021 = 407,021
and
-1 x -407,021 = 407,021
Notice both answers equal 407,021
With that explanation out of the way, let's continue. Next, we take the number 407,021 and divide it by 2:
407,021 ÷ 2 = 203,510.5
If the quotient is a whole number, then 2 and 203,510.5 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 | 407,021 | |
-1 | -407,021 |
Now, we try dividing 407,021 by 3:
407,021 ÷ 3 = 135,673.6667
If the quotient is a whole number, then 3 and 135,673.6667 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 | 407,021 | |
-1 | -407,021 |
Let's try dividing by 4:
407,021 ÷ 4 = 101,755.25
If the quotient is a whole number, then 4 and 101,755.25 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 | 407,021 | |
-1 | 407,021 |
If you did it right, you will end up with this table:
1 | 191 | 2,131 | 407,021 |
-1 | -191 | -2,131 | -407,021 |
Here are some more numbers to try:
Try the factor calculator