Q: What are the factor combinations of the number 305?
A:
Positive:
1 x 3055 x 61
Negative:
-1 x -305-5 x -61
A:
Positive:
1 x 3055 x 61
Negative:
-1 x -305-5 x -61
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 305, 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 | 305 | |
| -1 | -305 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 305.
Example:
1 x 305 = 305
and
-1 x -305 = 305
Notice both answers equal 305
With that explanation out of the way, let's continue. Next, we take the number 305 and divide it by 2:
305 ÷ 2 = 152.5
If the quotient is a whole number, then 2 and 152.5 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 | 305 | |
| -1 | -305 |
Now, we try dividing 305 by 3:
305 ÷ 3 = 101.6667
If the quotient is a whole number, then 3 and 101.6667 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 | 305 | |
| -1 | -305 |
Let's try dividing by 4:
305 ÷ 4 = 76.25
If the quotient is a whole number, then 4 and 76.25 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 | 305 | |
| -1 | 305 |
If you did it right, you will end up with this table:
| 1 | 5 | 61 | 305 |
| -1 | -5 | -61 | -305 |
Here are some more numbers to try:
Try the factor calculator