Q: What are the factor combinations of the number 167,209?
A:
Positive:
1 x 1672097 x 23887
Negative:
-1 x -167209-7 x -23887
A:
Positive:
1 x 1672097 x 23887
Negative:
-1 x -167209-7 x -23887
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 167,209, 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 | 167,209 | |
-1 | -167,209 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 167,209.
Example:
1 x 167,209 = 167,209
and
-1 x -167,209 = 167,209
Notice both answers equal 167,209
With that explanation out of the way, let's continue. Next, we take the number 167,209 and divide it by 2:
167,209 ÷ 2 = 83,604.5
If the quotient is a whole number, then 2 and 83,604.5 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 | 167,209 | |
-1 | -167,209 |
Now, we try dividing 167,209 by 3:
167,209 ÷ 3 = 55,736.3333
If the quotient is a whole number, then 3 and 55,736.3333 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 | 167,209 | |
-1 | -167,209 |
Let's try dividing by 4:
167,209 ÷ 4 = 41,802.25
If the quotient is a whole number, then 4 and 41,802.25 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 | 167,209 | |
-1 | 167,209 |
If you did it right, you will end up with this table:
1 | 7 | 23,887 | 167,209 |
-1 | -7 | -23,887 | -167,209 |
Here are some more numbers to try:
Try the factor calculator