Q: What are the factor combinations of the number 49?
A:
Positive:
1 x 497 x 7
Negative:
-1 x -49-7 x -7
A:
Positive:
1 x 497 x 7
Negative:
-1 x -49-7 x -7
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 49, 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 | 49 | |
| -1 | -49 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 49.
Example:
1 x 49 = 49
and
-1 x -49 = 49
Notice both answers equal 49
With that explanation out of the way, let's continue. Next, we take the number 49 and divide it by 2:
49 ÷ 2 = 24.5
If the quotient is a whole number, then 2 and 24.5 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 | 49 | |
| -1 | -49 |
Now, we try dividing 49 by 3:
49 ÷ 3 = 16.3333
If the quotient is a whole number, then 3 and 16.3333 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 | 49 | |
| -1 | -49 |
Let's try dividing by 4:
49 ÷ 4 = 12.25
If the quotient is a whole number, then 4 and 12.25 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 | 49 | |
| -1 | 49 |
If you did it right, you will end up with this table:
| 1 | 7 | 49 |
| -1 | -7 | -49 |
Here are some more numbers to try:
Try the factor calculator