Q: What are the factor combinations of the number 357,336,721?

 A:
Positive:   1 x 3573367217 x 5104810331 x 11526991217 x 1646713683 x 5231872411 x 1482114781 x 7474116877 x 21173
Negative: -1 x -357336721-7 x -51048103-31 x -11526991-217 x -1646713-683 x -523187-2411 x -148211-4781 x -74741-16877 x -21173


How do I find the factor combinations of the number 357,336,721?

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 357,336,721, 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.

1 357,336,721
-1 -357,336,721

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 357,336,721.

Example:
1 x 357,336,721 = 357,336,721
and
-1 x -357,336,721 = 357,336,721
Notice both answers equal 357,336,721

With that explanation out of the way, let's continue. Next, we take the number 357,336,721 and divide it by 2:

357,336,721 ÷ 2 = 178,668,360.5

If the quotient is a whole number, then 2 and 178,668,360.5 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:

1 357,336,721
-1 -357,336,721

Now, we try dividing 357,336,721 by 3:

357,336,721 ÷ 3 = 119,112,240.3333

If the quotient is a whole number, then 3 and 119,112,240.3333 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:

1 357,336,721
-1 -357,336,721

Let's try dividing by 4:

357,336,721 ÷ 4 = 89,334,180.25

If the quotient is a whole number, then 4 and 89,334,180.25 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:

1 357,336,721
-1 357,336,721
Keep dividing by the next highest number until you cannot divide anymore.

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

17312176832,4114,78116,87721,17374,741148,211523,1871,646,71311,526,99151,048,103357,336,721
-1-7-31-217-683-2,411-4,781-16,877-21,173-74,741-148,211-523,187-1,646,713-11,526,991-51,048,103-357,336,721

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