Q: What are the factor combinations of the number 120,901?

 A:
Positive:   1 x 12090111 x 1099129 x 4169319 x 379
Negative: -1 x -120901-11 x -10991-29 x -4169-319 x -379


How do I find the factor combinations of the number 120,901?

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 120,901, 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.

1 120,901
-1 -120,901

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 120,901.

Example:
1 x 120,901 = 120,901
and
-1 x -120,901 = 120,901
Notice both answers equal 120,901

With that explanation out of the way, let's continue. Next, we take the number 120,901 and divide it by 2:

120,901 ÷ 2 = 60,450.5

If the quotient is a whole number, then 2 and 60,450.5 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:

1 120,901
-1 -120,901

Now, we try dividing 120,901 by 3:

120,901 ÷ 3 = 40,300.3333

If the quotient is a whole number, then 3 and 40,300.3333 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:

1 120,901
-1 -120,901

Let's try dividing by 4:

120,901 ÷ 4 = 30,225.25

If the quotient is a whole number, then 4 and 30,225.25 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:

1 120,901
-1 120,901
Keep dividing by the next highest number until you cannot divide anymore.

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

111293193794,16910,991120,901
-1-11-29-319-379-4,169-10,991-120,901

More Examples

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