Q: What are the factor combinations of the number 12,162,973?

 A:
Positive:   1 x 1216297317 x 71546937 x 32872961 x 199393317 x 38369629 x 193371037 x 117292257 x 5389
Negative: -1 x -12162973-17 x -715469-37 x -328729-61 x -199393-317 x -38369-629 x -19337-1037 x -11729-2257 x -5389


How do I find the factor combinations of the number 12,162,973?

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 12,162,973, 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 12,162,973
-1 -12,162,973

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 12,162,973.

Example:
1 x 12,162,973 = 12,162,973
and
-1 x -12,162,973 = 12,162,973
Notice both answers equal 12,162,973

With that explanation out of the way, let's continue. Next, we take the number 12,162,973 and divide it by 2:

12,162,973 ÷ 2 = 6,081,486.5

If the quotient is a whole number, then 2 and 6,081,486.5 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 12,162,973
-1 -12,162,973

Now, we try dividing 12,162,973 by 3:

12,162,973 ÷ 3 = 4,054,324.3333

If the quotient is a whole number, then 3 and 4,054,324.3333 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 12,162,973
-1 -12,162,973

Let's try dividing by 4:

12,162,973 ÷ 4 = 3,040,743.25

If the quotient is a whole number, then 4 and 3,040,743.25 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 12,162,973
-1 12,162,973
Keep dividing by the next highest number until you cannot divide anymore.

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

11737613176291,0372,2575,38911,72919,33738,369199,393328,729715,46912,162,973
-1-17-37-61-317-629-1,037-2,257-5,389-11,729-19,337-38,369-199,393-328,729-715,469-12,162,973

More Examples

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