Q: What are the factor combinations of the number 120,396,397?

 A:
Positive:   1 x 12039639711 x 1094512717 x 708214183 x 1450559187 x 643831913 x 1318691411 x 853277757 x 15521
Negative: -1 x -120396397-11 x -10945127-17 x -7082141-83 x -1450559-187 x -643831-913 x -131869-1411 x -85327-7757 x -15521


How do I find the factor combinations of the number 120,396,397?

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 120,396,397, 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.

1 120,396,397
-1 -120,396,397

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 120,396,397.

Example:
1 x 120,396,397 = 120,396,397
and
-1 x -120,396,397 = 120,396,397
Notice both answers equal 120,396,397

With that explanation out of the way, let's continue. Next, we take the number 120,396,397 and divide it by 2:

120,396,397 ÷ 2 = 60,198,198.5

If the quotient is a whole number, then 2 and 60,198,198.5 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:

1 120,396,397
-1 -120,396,397

Now, we try dividing 120,396,397 by 3:

120,396,397 ÷ 3 = 40,132,132.3333

If the quotient is a whole number, then 3 and 40,132,132.3333 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:

1 120,396,397
-1 -120,396,397

Let's try dividing by 4:

120,396,397 ÷ 4 = 30,099,099.25

If the quotient is a whole number, then 4 and 30,099,099.25 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:

1 120,396,397
-1 120,396,397
Keep dividing by the next highest number until you cannot divide anymore.

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

11117831879131,4117,75715,52185,327131,869643,8311,450,5597,082,14110,945,127120,396,397
-1-11-17-83-187-913-1,411-7,757-15,521-85,327-131,869-643,831-1,450,559-7,082,141-10,945,127-120,396,397

More Examples

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