Q: What are the factor combinations of the number 213,517?
A:
Positive:
1 x 213517149 x 1433
Negative:
-1 x -213517-149 x -1433
A:
Positive:
1 x 213517149 x 1433
Negative:
-1 x -213517-149 x -1433
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 213,517, 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 | 213,517 | |
-1 | -213,517 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 213,517.
Example:
1 x 213,517 = 213,517
and
-1 x -213,517 = 213,517
Notice both answers equal 213,517
With that explanation out of the way, let's continue. Next, we take the number 213,517 and divide it by 2:
213,517 ÷ 2 = 106,758.5
If the quotient is a whole number, then 2 and 106,758.5 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 | 213,517 | |
-1 | -213,517 |
Now, we try dividing 213,517 by 3:
213,517 ÷ 3 = 71,172.3333
If the quotient is a whole number, then 3 and 71,172.3333 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 | 213,517 | |
-1 | -213,517 |
Let's try dividing by 4:
213,517 ÷ 4 = 53,379.25
If the quotient is a whole number, then 4 and 53,379.25 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 | 213,517 | |
-1 | 213,517 |
If you did it right, you will end up with this table:
1 | 149 | 1,433 | 213,517 |
-1 | -149 | -1,433 | -213,517 |
Here are some more numbers to try:
Try the factor calculator