Q: What are the factor combinations of the number 20,975?

 A:
Positive:   1 x 209755 x 419525 x 839
Negative: -1 x -20975-5 x -4195-25 x -839


How do I find the factor combinations of the number 20,975?

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 20,975, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

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 20,975
-1 -20,975

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 20,975.

Example:
1 x 20,975 = 20,975
and
-1 x -20,975 = 20,975
Notice both answers equal 20,975

With that explanation out of the way, let's continue. Next, we take the number 20,975 and divide it by 2:

20,975 ÷ 2 = 10,487.5

If the quotient is a whole number, then 2 and 10,487.5 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 20,975
-1 -20,975

Now, we try dividing 20,975 by 3:

20,975 ÷ 3 = 6,991.6667

If the quotient is a whole number, then 3 and 6,991.6667 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 20,975
-1 -20,975

Let's try dividing by 4:

20,975 ÷ 4 = 5,243.75

If the quotient is a whole number, then 4 and 5,243.75 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 20,975
-1 20,975
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

15258394,19520,975
-1-5-25-839-4,195-20,975

More Examples

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