Q: What are the factor combinations of the number 30,709?
A:
Positive:
1 x 307097 x 438741 x 749107 x 287
Negative:
-1 x -30709-7 x -4387-41 x -749-107 x -287
A:
Positive:
1 x 307097 x 438741 x 749107 x 287
Negative:
-1 x -30709-7 x -4387-41 x -749-107 x -287
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 30,709, 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 | 30,709 | |
-1 | -30,709 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 30,709.
Example:
1 x 30,709 = 30,709
and
-1 x -30,709 = 30,709
Notice both answers equal 30,709
With that explanation out of the way, let's continue. Next, we take the number 30,709 and divide it by 2:
30,709 ÷ 2 = 15,354.5
If the quotient is a whole number, then 2 and 15,354.5 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 | 30,709 | |
-1 | -30,709 |
Now, we try dividing 30,709 by 3:
30,709 ÷ 3 = 10,236.3333
If the quotient is a whole number, then 3 and 10,236.3333 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 | 30,709 | |
-1 | -30,709 |
Let's try dividing by 4:
30,709 ÷ 4 = 7,677.25
If the quotient is a whole number, then 4 and 7,677.25 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 | 30,709 | |
-1 | 30,709 |
If you did it right, you will end up with this table:
1 | 7 | 41 | 107 | 287 | 749 | 4,387 | 30,709 |
-1 | -7 | -41 | -107 | -287 | -749 | -4,387 | -30,709 |
Here are some more numbers to try:
Try the factor calculator