Q: What are the factor combinations of the number 313,047,361?

 A:
Positive:   1 x 31304736111 x 28458851149 x 2100989389 x 804749491 x 6375711639 x 1909994279 x 731595401 x 57961
Negative: -1 x -313047361-11 x -28458851-149 x -2100989-389 x -804749-491 x -637571-1639 x -190999-4279 x -73159-5401 x -57961


How do I find the factor combinations of the number 313,047,361?

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 313,047,361, 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.

1 313,047,361
-1 -313,047,361

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 313,047,361.

Example:
1 x 313,047,361 = 313,047,361
and
-1 x -313,047,361 = 313,047,361
Notice both answers equal 313,047,361

With that explanation out of the way, let's continue. Next, we take the number 313,047,361 and divide it by 2:

313,047,361 ÷ 2 = 156,523,680.5

If the quotient is a whole number, then 2 and 156,523,680.5 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:

1 313,047,361
-1 -313,047,361

Now, we try dividing 313,047,361 by 3:

313,047,361 ÷ 3 = 104,349,120.3333

If the quotient is a whole number, then 3 and 104,349,120.3333 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:

1 313,047,361
-1 -313,047,361

Let's try dividing by 4:

313,047,361 ÷ 4 = 78,261,840.25

If the quotient is a whole number, then 4 and 78,261,840.25 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:

1 313,047,361
-1 313,047,361
Keep dividing by the next highest number until you cannot divide anymore.

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

1111493894911,6394,2795,40157,96173,159190,999637,571804,7492,100,98928,458,851313,047,361
-1-11-149-389-491-1,639-4,279-5,401-57,961-73,159-190,999-637,571-804,749-2,100,989-28,458,851-313,047,361

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