Q: What are the factor combinations of the number 120,230,131?

 A:
Positive:   1 x 1202301317 x 1717573323 x 522739737 x 3249463161 x 746771259 x 464209851 x 1412815957 x 20183
Negative: -1 x -120230131-7 x -17175733-23 x -5227397-37 x -3249463-161 x -746771-259 x -464209-851 x -141281-5957 x -20183


How do I find the factor combinations of the number 120,230,131?

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 120,230,131, 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.

1 120,230,131
-1 -120,230,131

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 120,230,131.

Example:
1 x 120,230,131 = 120,230,131
and
-1 x -120,230,131 = 120,230,131
Notice both answers equal 120,230,131

With that explanation out of the way, let's continue. Next, we take the number 120,230,131 and divide it by 2:

120,230,131 ÷ 2 = 60,115,065.5

If the quotient is a whole number, then 2 and 60,115,065.5 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:

1 120,230,131
-1 -120,230,131

Now, we try dividing 120,230,131 by 3:

120,230,131 ÷ 3 = 40,076,710.3333

If the quotient is a whole number, then 3 and 40,076,710.3333 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:

1 120,230,131
-1 -120,230,131

Let's try dividing by 4:

120,230,131 ÷ 4 = 30,057,532.75

If the quotient is a whole number, then 4 and 30,057,532.75 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:

1 120,230,131
-1 120,230,131
Keep dividing by the next highest number until you cannot divide anymore.

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

1723371612598515,95720,183141,281464,209746,7713,249,4635,227,39717,175,733120,230,131
-1-7-23-37-161-259-851-5,957-20,183-141,281-464,209-746,771-3,249,463-5,227,397-17,175,733-120,230,131

More Examples

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