Q: What are the factor combinations of the number 312,432,115?

 A:
Positive:   1 x 3124321155 x 6248642323 x 13584005115 x 2716801677 x 4614953385 x 922994013 x 7785515571 x 20065
Negative: -1 x -312432115-5 x -62486423-23 x -13584005-115 x -2716801-677 x -461495-3385 x -92299-4013 x -77855-15571 x -20065


How do I find the factor combinations of the number 312,432,115?

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 312,432,115, 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.

1 312,432,115
-1 -312,432,115

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 312,432,115.

Example:
1 x 312,432,115 = 312,432,115
and
-1 x -312,432,115 = 312,432,115
Notice both answers equal 312,432,115

With that explanation out of the way, let's continue. Next, we take the number 312,432,115 and divide it by 2:

312,432,115 ÷ 2 = 156,216,057.5

If the quotient is a whole number, then 2 and 156,216,057.5 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:

1 312,432,115
-1 -312,432,115

Now, we try dividing 312,432,115 by 3:

312,432,115 ÷ 3 = 104,144,038.3333

If the quotient is a whole number, then 3 and 104,144,038.3333 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:

1 312,432,115
-1 -312,432,115

Let's try dividing by 4:

312,432,115 ÷ 4 = 78,108,028.75

If the quotient is a whole number, then 4 and 78,108,028.75 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:

1 312,432,115
-1 312,432,115
Keep dividing by the next highest number until you cannot divide anymore.

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

15231156773,3854,01315,57120,06577,85592,299461,4952,716,80113,584,00562,486,423312,432,115
-1-5-23-115-677-3,385-4,013-15,571-20,065-77,855-92,299-461,495-2,716,801-13,584,005-62,486,423-312,432,115

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