Q: What are the factor combinations of the number 8,300,131?

 A:
Positive:   1 x 83001317 x 118573317 x 48824319 x 436849119 x 69749133 x 62407323 x 256972261 x 3671
Negative: -1 x -8300131-7 x -1185733-17 x -488243-19 x -436849-119 x -69749-133 x -62407-323 x -25697-2261 x -3671


How do I find the factor combinations of the number 8,300,131?

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 8,300,131, 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 8,300,131
-1 -8,300,131

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 8,300,131.

Example:
1 x 8,300,131 = 8,300,131
and
-1 x -8,300,131 = 8,300,131
Notice both answers equal 8,300,131

With that explanation out of the way, let's continue. Next, we take the number 8,300,131 and divide it by 2:

8,300,131 ÷ 2 = 4,150,065.5

If the quotient is a whole number, then 2 and 4,150,065.5 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 8,300,131
-1 -8,300,131

Now, we try dividing 8,300,131 by 3:

8,300,131 ÷ 3 = 2,766,710.3333

If the quotient is a whole number, then 3 and 2,766,710.3333 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 8,300,131
-1 -8,300,131

Let's try dividing by 4:

8,300,131 ÷ 4 = 2,075,032.75

If the quotient is a whole number, then 4 and 2,075,032.75 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 8,300,131
-1 8,300,131
Keep dividing by the next highest number until you cannot divide anymore.

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

1717191191333232,2613,67125,69762,40769,749436,849488,2431,185,7338,300,131
-1-7-17-19-119-133-323-2,261-3,671-25,697-62,407-69,749-436,849-488,243-1,185,733-8,300,131

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