Q: What are the factor combinations of the number 313,100,297?

 A:
Positive:   1 x 31310029719 x 16478963107 x 2926171337 x 929081457 x 6851212033 x 1540096403 x 488998683 x 36059
Negative: -1 x -313100297-19 x -16478963-107 x -2926171-337 x -929081-457 x -685121-2033 x -154009-6403 x -48899-8683 x -36059


How do I find the factor combinations of the number 313,100,297?

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 313,100,297, 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.

1 313,100,297
-1 -313,100,297

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 313,100,297.

Example:
1 x 313,100,297 = 313,100,297
and
-1 x -313,100,297 = 313,100,297
Notice both answers equal 313,100,297

With that explanation out of the way, let's continue. Next, we take the number 313,100,297 and divide it by 2:

313,100,297 ÷ 2 = 156,550,148.5

If the quotient is a whole number, then 2 and 156,550,148.5 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:

1 313,100,297
-1 -313,100,297

Now, we try dividing 313,100,297 by 3:

313,100,297 ÷ 3 = 104,366,765.6667

If the quotient is a whole number, then 3 and 104,366,765.6667 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:

1 313,100,297
-1 -313,100,297

Let's try dividing by 4:

313,100,297 ÷ 4 = 78,275,074.25

If the quotient is a whole number, then 4 and 78,275,074.25 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:

1 313,100,297
-1 313,100,297
Keep dividing by the next highest number until you cannot divide anymore.

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

1191073374572,0336,4038,68336,05948,899154,009685,121929,0812,926,17116,478,963313,100,297
-1-19-107-337-457-2,033-6,403-8,683-36,059-48,899-154,009-685,121-929,081-2,926,171-16,478,963-313,100,297

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