Q: What are the factor combinations of the number 312,340,715?

 A:
Positive:   1 x 3123407155 x 6246814319 x 1643898571 x 439916595 x 3287797355 x 8798331349 x 2315356745 x 46307
Negative: -1 x -312340715-5 x -62468143-19 x -16438985-71 x -4399165-95 x -3287797-355 x -879833-1349 x -231535-6745 x -46307


How do I find the factor combinations of the number 312,340,715?

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 312,340,715, 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.

1 312,340,715
-1 -312,340,715

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 312,340,715.

Example:
1 x 312,340,715 = 312,340,715
and
-1 x -312,340,715 = 312,340,715
Notice both answers equal 312,340,715

With that explanation out of the way, let's continue. Next, we take the number 312,340,715 and divide it by 2:

312,340,715 ÷ 2 = 156,170,357.5

If the quotient is a whole number, then 2 and 156,170,357.5 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:

1 312,340,715
-1 -312,340,715

Now, we try dividing 312,340,715 by 3:

312,340,715 ÷ 3 = 104,113,571.6667

If the quotient is a whole number, then 3 and 104,113,571.6667 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:

1 312,340,715
-1 -312,340,715

Let's try dividing by 4:

312,340,715 ÷ 4 = 78,085,178.75

If the quotient is a whole number, then 4 and 78,085,178.75 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:

1 312,340,715
-1 312,340,715
Keep dividing by the next highest number until you cannot divide anymore.

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

151971953551,3496,74546,307231,535879,8333,287,7974,399,16516,438,98562,468,143312,340,715
-1-5-19-71-95-355-1,349-6,745-46,307-231,535-879,833-3,287,797-4,399,165-16,438,985-62,468,143-312,340,715

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