Q: What are the factor combinations of the number 131,303,029?

 A:
Positive:   1 x 13130302911 x 1193663913 x 10100233121 x 1085149143 x 918203169 x 7769411573 x 834731859 x 706316421 x 20449
Negative: -1 x -131303029-11 x -11936639-13 x -10100233-121 x -1085149-143 x -918203-169 x -776941-1573 x -83473-1859 x -70631-6421 x -20449


How do I find the factor combinations of the number 131,303,029?

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 131,303,029, 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.

1 131,303,029
-1 -131,303,029

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 131,303,029.

Example:
1 x 131,303,029 = 131,303,029
and
-1 x -131,303,029 = 131,303,029
Notice both answers equal 131,303,029

With that explanation out of the way, let's continue. Next, we take the number 131,303,029 and divide it by 2:

131,303,029 ÷ 2 = 65,651,514.5

If the quotient is a whole number, then 2 and 65,651,514.5 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:

1 131,303,029
-1 -131,303,029

Now, we try dividing 131,303,029 by 3:

131,303,029 ÷ 3 = 43,767,676.3333

If the quotient is a whole number, then 3 and 43,767,676.3333 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:

1 131,303,029
-1 -131,303,029

Let's try dividing by 4:

131,303,029 ÷ 4 = 32,825,757.25

If the quotient is a whole number, then 4 and 32,825,757.25 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:

1 131,303,029
-1 131,303,029
Keep dividing by the next highest number until you cannot divide anymore.

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

111131211431691,5731,8596,42120,44970,63183,473776,941918,2031,085,14910,100,23311,936,639131,303,029
-1-11-13-121-143-169-1,573-1,859-6,421-20,449-70,631-83,473-776,941-918,203-1,085,149-10,100,233-11,936,639-131,303,029

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