Q: What are the factor combinations of the number 121,022,209?

 A:
Positive:   1 x 1210222097 x 1728888711 x 1100201949 x 246984177 x 1571717113 x 1070993539 x 224531791 x 1529991243 x 973631987 x 609075537 x 218578701 x 13909
Negative: -1 x -121022209-7 x -17288887-11 x -11002019-49 x -2469841-77 x -1571717-113 x -1070993-539 x -224531-791 x -152999-1243 x -97363-1987 x -60907-5537 x -21857-8701 x -13909


How do I find the factor combinations of the number 121,022,209?

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 121,022,209, 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.

1 121,022,209
-1 -121,022,209

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 121,022,209.

Example:
1 x 121,022,209 = 121,022,209
and
-1 x -121,022,209 = 121,022,209
Notice both answers equal 121,022,209

With that explanation out of the way, let's continue. Next, we take the number 121,022,209 and divide it by 2:

121,022,209 ÷ 2 = 60,511,104.5

If the quotient is a whole number, then 2 and 60,511,104.5 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:

1 121,022,209
-1 -121,022,209

Now, we try dividing 121,022,209 by 3:

121,022,209 ÷ 3 = 40,340,736.3333

If the quotient is a whole number, then 3 and 40,340,736.3333 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:

1 121,022,209
-1 -121,022,209

Let's try dividing by 4:

121,022,209 ÷ 4 = 30,255,552.25

If the quotient is a whole number, then 4 and 30,255,552.25 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:

1 121,022,209
-1 121,022,209
Keep dividing by the next highest number until you cannot divide anymore.

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

171149771135397911,2431,9875,5378,70113,90921,85760,90797,363152,999224,5311,070,9931,571,7172,469,84111,002,01917,288,887121,022,209
-1-7-11-49-77-113-539-791-1,243-1,987-5,537-8,701-13,909-21,857-60,907-97,363-152,999-224,531-1,070,993-1,571,717-2,469,841-11,002,019-17,288,887-121,022,209

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