Q: What are the factor combinations of the number 212,371?
A:
Positive:
1 x 21237153 x 4007
Negative:
-1 x -212371-53 x -4007
A:
Positive:
1 x 21237153 x 4007
Negative:
-1 x -212371-53 x -4007
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 212,371, 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 | 212,371 | |
-1 | -212,371 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 212,371.
Example:
1 x 212,371 = 212,371
and
-1 x -212,371 = 212,371
Notice both answers equal 212,371
With that explanation out of the way, let's continue. Next, we take the number 212,371 and divide it by 2:
212,371 ÷ 2 = 106,185.5
If the quotient is a whole number, then 2 and 106,185.5 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 | 212,371 | |
-1 | -212,371 |
Now, we try dividing 212,371 by 3:
212,371 ÷ 3 = 70,790.3333
If the quotient is a whole number, then 3 and 70,790.3333 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 | 212,371 | |
-1 | -212,371 |
Let's try dividing by 4:
212,371 ÷ 4 = 53,092.75
If the quotient is a whole number, then 4 and 53,092.75 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 | 212,371 | |
-1 | 212,371 |
If you did it right, you will end up with this table:
1 | 53 | 4,007 | 212,371 |
-1 | -53 | -4,007 | -212,371 |
Here are some more numbers to try:
Try the factor calculator