Q: What are the factor combinations of the number 121,211,209?

 A:
Positive:   1 x 1212112097 x 1731588731 x 391003961 x 1987069217 x 558577427 x 2838671891 x 640999157 x 13237
Negative: -1 x -121211209-7 x -17315887-31 x -3910039-61 x -1987069-217 x -558577-427 x -283867-1891 x -64099-9157 x -13237


How do I find the factor combinations of the number 121,211,209?

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 121,211,209, 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.

1 121,211,209
-1 -121,211,209

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 121,211,209.

Example:
1 x 121,211,209 = 121,211,209
and
-1 x -121,211,209 = 121,211,209
Notice both answers equal 121,211,209

With that explanation out of the way, let's continue. Next, we take the number 121,211,209 and divide it by 2:

121,211,209 ÷ 2 = 60,605,604.5

If the quotient is a whole number, then 2 and 60,605,604.5 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:

1 121,211,209
-1 -121,211,209

Now, we try dividing 121,211,209 by 3:

121,211,209 ÷ 3 = 40,403,736.3333

If the quotient is a whole number, then 3 and 40,403,736.3333 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:

1 121,211,209
-1 -121,211,209

Let's try dividing by 4:

121,211,209 ÷ 4 = 30,302,802.25

If the quotient is a whole number, then 4 and 30,302,802.25 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:

1 121,211,209
-1 121,211,209
Keep dividing by the next highest number until you cannot divide anymore.

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

1731612174271,8919,15713,23764,099283,867558,5771,987,0693,910,03917,315,887121,211,209
-1-7-31-61-217-427-1,891-9,157-13,237-64,099-283,867-558,577-1,987,069-3,910,039-17,315,887-121,211,209

More Examples

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