Q: What are the factor combinations of the number 352,002,119?

 A:
Positive:   1 x 3520021197 x 5028601717 x 20706007113 x 3115063119 x 2958001791 x 4450091921 x 18323913447 x 26177
Negative: -1 x -352002119-7 x -50286017-17 x -20706007-113 x -3115063-119 x -2958001-791 x -445009-1921 x -183239-13447 x -26177


How do I find the factor combinations of the number 352,002,119?

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 352,002,119, 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.

1 352,002,119
-1 -352,002,119

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 352,002,119.

Example:
1 x 352,002,119 = 352,002,119
and
-1 x -352,002,119 = 352,002,119
Notice both answers equal 352,002,119

With that explanation out of the way, let's continue. Next, we take the number 352,002,119 and divide it by 2:

352,002,119 ÷ 2 = 176,001,059.5

If the quotient is a whole number, then 2 and 176,001,059.5 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:

1 352,002,119
-1 -352,002,119

Now, we try dividing 352,002,119 by 3:

352,002,119 ÷ 3 = 117,334,039.6667

If the quotient is a whole number, then 3 and 117,334,039.6667 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:

1 352,002,119
-1 -352,002,119

Let's try dividing by 4:

352,002,119 ÷ 4 = 88,000,529.75

If the quotient is a whole number, then 4 and 88,000,529.75 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:

1 352,002,119
-1 352,002,119
Keep dividing by the next highest number until you cannot divide anymore.

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

17171131197911,92113,44726,177183,239445,0092,958,0013,115,06320,706,00750,286,017352,002,119
-1-7-17-113-119-791-1,921-13,447-26,177-183,239-445,009-2,958,001-3,115,063-20,706,007-50,286,017-352,002,119

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