Q: What are the factor combinations of the number 23,075?

 A:
Positive:   1 x 230755 x 461513 x 177525 x 92365 x 35571 x 325
Negative: -1 x -23075-5 x -4615-13 x -1775-25 x -923-65 x -355-71 x -325


How do I find the factor combinations of the number 23,075?

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 23,075, 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 23,075
-1 -23,075

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 23,075.

Example:
1 x 23,075 = 23,075
and
-1 x -23,075 = 23,075
Notice both answers equal 23,075

With that explanation out of the way, let's continue. Next, we take the number 23,075 and divide it by 2:

23,075 ÷ 2 = 11,537.5

If the quotient is a whole number, then 2 and 11,537.5 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 23,075
-1 -23,075

Now, we try dividing 23,075 by 3:

23,075 ÷ 3 = 7,691.6667

If the quotient is a whole number, then 3 and 7,691.6667 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 23,075
-1 -23,075

Let's try dividing by 4:

23,075 ÷ 4 = 5,768.75

If the quotient is a whole number, then 4 and 5,768.75 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 23,075
-1 23,075
Keep dividing by the next highest number until you cannot divide anymore.

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

15132565713253559231,7754,61523,075
-1-5-13-25-65-71-325-355-923-1,775-4,615-23,075

More Examples

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