Q: What are the factor combinations of the number 12,175?

 A:
Positive:   1 x 121755 x 243525 x 487
Negative: -1 x -12175-5 x -2435-25 x -487


How do I find the factor combinations of the number 12,175?

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 12,175, 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 12,175
-1 -12,175

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 12,175.

Example:
1 x 12,175 = 12,175
and
-1 x -12,175 = 12,175
Notice both answers equal 12,175

With that explanation out of the way, let's continue. Next, we take the number 12,175 and divide it by 2:

12,175 ÷ 2 = 6,087.5

If the quotient is a whole number, then 2 and 6,087.5 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 12,175
-1 -12,175

Now, we try dividing 12,175 by 3:

12,175 ÷ 3 = 4,058.3333

If the quotient is a whole number, then 3 and 4,058.3333 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 12,175
-1 -12,175

Let's try dividing by 4:

12,175 ÷ 4 = 3,043.75

If the quotient is a whole number, then 4 and 3,043.75 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 12,175
-1 12,175
Keep dividing by the next highest number until you cannot divide anymore.

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

15254872,43512,175
-1-5-25-487-2,435-12,175

More Examples

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