Q: What are the factor combinations of the number 212,509?
A:
Positive:
1 x 21250911 x 19319
Negative:
-1 x -212509-11 x -19319
A:
Positive:
1 x 21250911 x 19319
Negative:
-1 x -212509-11 x -19319
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 212,509, 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 | 212,509 | |
-1 | -212,509 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 212,509.
Example:
1 x 212,509 = 212,509
and
-1 x -212,509 = 212,509
Notice both answers equal 212,509
With that explanation out of the way, let's continue. Next, we take the number 212,509 and divide it by 2:
212,509 ÷ 2 = 106,254.5
If the quotient is a whole number, then 2 and 106,254.5 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 | 212,509 | |
-1 | -212,509 |
Now, we try dividing 212,509 by 3:
212,509 ÷ 3 = 70,836.3333
If the quotient is a whole number, then 3 and 70,836.3333 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 | 212,509 | |
-1 | -212,509 |
Let's try dividing by 4:
212,509 ÷ 4 = 53,127.25
If the quotient is a whole number, then 4 and 53,127.25 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 | 212,509 | |
-1 | 212,509 |
If you did it right, you will end up with this table:
1 | 11 | 19,319 | 212,509 |
-1 | -11 | -19,319 | -212,509 |
Here are some more numbers to try:
Try the factor calculator