Q: What are the factor combinations of the number 82,509,313?

 A:
Positive:   1 x 8250931317 x 485348971 x 1162103197 x 418829347 x 2377791207 x 683593349 x 246375899 x 13987
Negative: -1 x -82509313-17 x -4853489-71 x -1162103-197 x -418829-347 x -237779-1207 x -68359-3349 x -24637-5899 x -13987


How do I find the factor combinations of the number 82,509,313?

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 82,509,313, 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 82,509,313
-1 -82,509,313

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 82,509,313.

Example:
1 x 82,509,313 = 82,509,313
and
-1 x -82,509,313 = 82,509,313
Notice both answers equal 82,509,313

With that explanation out of the way, let's continue. Next, we take the number 82,509,313 and divide it by 2:

82,509,313 ÷ 2 = 41,254,656.5

If the quotient is a whole number, then 2 and 41,254,656.5 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 82,509,313
-1 -82,509,313

Now, we try dividing 82,509,313 by 3:

82,509,313 ÷ 3 = 27,503,104.3333

If the quotient is a whole number, then 3 and 27,503,104.3333 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 82,509,313
-1 -82,509,313

Let's try dividing by 4:

82,509,313 ÷ 4 = 20,627,328.25

If the quotient is a whole number, then 4 and 20,627,328.25 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 82,509,313
-1 82,509,313
Keep dividing by the next highest number until you cannot divide anymore.

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

117711973471,2073,3495,89913,98724,63768,359237,779418,8291,162,1034,853,48982,509,313
-1-17-71-197-347-1,207-3,349-5,899-13,987-24,637-68,359-237,779-418,829-1,162,103-4,853,489-82,509,313

More Examples

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