Q: What are the factor combinations of the number 357,102,317?

 A:
Positive:   1 x 35710231711 x 3246384713 x 2746940929 x 12313873143 x 2497219319 x 1119443377 x 9472214147 x 86111
Negative: -1 x -357102317-11 x -32463847-13 x -27469409-29 x -12313873-143 x -2497219-319 x -1119443-377 x -947221-4147 x -86111


How do I find the factor combinations of the number 357,102,317?

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 357,102,317, 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.

1 357,102,317
-1 -357,102,317

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 357,102,317.

Example:
1 x 357,102,317 = 357,102,317
and
-1 x -357,102,317 = 357,102,317
Notice both answers equal 357,102,317

With that explanation out of the way, let's continue. Next, we take the number 357,102,317 and divide it by 2:

357,102,317 ÷ 2 = 178,551,158.5

If the quotient is a whole number, then 2 and 178,551,158.5 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:

1 357,102,317
-1 -357,102,317

Now, we try dividing 357,102,317 by 3:

357,102,317 ÷ 3 = 119,034,105.6667

If the quotient is a whole number, then 3 and 119,034,105.6667 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:

1 357,102,317
-1 -357,102,317

Let's try dividing by 4:

357,102,317 ÷ 4 = 89,275,579.25

If the quotient is a whole number, then 4 and 89,275,579.25 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:

1 357,102,317
-1 357,102,317
Keep dividing by the next highest number until you cannot divide anymore.

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

11113291433193774,14786,111947,2211,119,4432,497,21912,313,87327,469,40932,463,847357,102,317
-1-11-13-29-143-319-377-4,147-86,111-947,221-1,119,443-2,497,219-12,313,873-27,469,409-32,463,847-357,102,317

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