Q: What are the factor combinations of the number 121,211,207?

 A:
Positive:   1 x 12121120713 x 932393917 x 7130071221 x 548467331 x 3661971657 x 731514303 x 281695627 x 21541
Negative: -1 x -121211207-13 x -9323939-17 x -7130071-221 x -548467-331 x -366197-1657 x -73151-4303 x -28169-5627 x -21541


How do I find the factor combinations of the number 121,211,207?

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 121,211,207, 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.

1 121,211,207
-1 -121,211,207

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 121,211,207.

Example:
1 x 121,211,207 = 121,211,207
and
-1 x -121,211,207 = 121,211,207
Notice both answers equal 121,211,207

With that explanation out of the way, let's continue. Next, we take the number 121,211,207 and divide it by 2:

121,211,207 ÷ 2 = 60,605,603.5

If the quotient is a whole number, then 2 and 60,605,603.5 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:

1 121,211,207
-1 -121,211,207

Now, we try dividing 121,211,207 by 3:

121,211,207 ÷ 3 = 40,403,735.6667

If the quotient is a whole number, then 3 and 40,403,735.6667 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:

1 121,211,207
-1 -121,211,207

Let's try dividing by 4:

121,211,207 ÷ 4 = 30,302,801.75

If the quotient is a whole number, then 4 and 30,302,801.75 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:

1 121,211,207
-1 121,211,207
Keep dividing by the next highest number until you cannot divide anymore.

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

113172213311,6574,3035,62721,54128,16973,151366,197548,4677,130,0719,323,939121,211,207
-1-13-17-221-331-1,657-4,303-5,627-21,541-28,169-73,151-366,197-548,467-7,130,071-9,323,939-121,211,207

More Examples

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