Q: What are the factor combinations of the number 121,099?

 A:
Positive:   1 x 12109911 x 11009101 x 1199109 x 1111
Negative: -1 x -121099-11 x -11009-101 x -1199-109 x -1111


How do I find the factor combinations of the number 121,099?

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 121,099, 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.

1 121,099
-1 -121,099

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 121,099.

Example:
1 x 121,099 = 121,099
and
-1 x -121,099 = 121,099
Notice both answers equal 121,099

With that explanation out of the way, let's continue. Next, we take the number 121,099 and divide it by 2:

121,099 ÷ 2 = 60,549.5

If the quotient is a whole number, then 2 and 60,549.5 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:

1 121,099
-1 -121,099

Now, we try dividing 121,099 by 3:

121,099 ÷ 3 = 40,366.3333

If the quotient is a whole number, then 3 and 40,366.3333 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:

1 121,099
-1 -121,099

Let's try dividing by 4:

121,099 ÷ 4 = 30,274.75

If the quotient is a whole number, then 4 and 30,274.75 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:

1 121,099
-1 121,099
Keep dividing by the next highest number until you cannot divide anymore.

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

1111011091,1111,19911,009121,099
-1-11-101-109-1,111-1,199-11,009-121,099

More Examples

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