Q: What are the factor combinations of the number 352,121,119?

 A:
Positive:   1 x 3521211197 x 5030301717 x 2071300737 x 9516787119 x 2959001259 x 1359541629 x 5598114403 x 79973
Negative: -1 x -352121119-7 x -50303017-17 x -20713007-37 x -9516787-119 x -2959001-259 x -1359541-629 x -559811-4403 x -79973


How do I find the factor combinations of the number 352,121,119?

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 352,121,119, 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.

1 352,121,119
-1 -352,121,119

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 352,121,119.

Example:
1 x 352,121,119 = 352,121,119
and
-1 x -352,121,119 = 352,121,119
Notice both answers equal 352,121,119

With that explanation out of the way, let's continue. Next, we take the number 352,121,119 and divide it by 2:

352,121,119 ÷ 2 = 176,060,559.5

If the quotient is a whole number, then 2 and 176,060,559.5 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:

1 352,121,119
-1 -352,121,119

Now, we try dividing 352,121,119 by 3:

352,121,119 ÷ 3 = 117,373,706.3333

If the quotient is a whole number, then 3 and 117,373,706.3333 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:

1 352,121,119
-1 -352,121,119

Let's try dividing by 4:

352,121,119 ÷ 4 = 88,030,279.75

If the quotient is a whole number, then 4 and 88,030,279.75 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:

1 352,121,119
-1 352,121,119
Keep dividing by the next highest number until you cannot divide anymore.

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

1717371192596294,40379,973559,8111,359,5412,959,0019,516,78720,713,00750,303,017352,121,119
-1-7-17-37-119-259-629-4,403-79,973-559,811-1,359,541-2,959,001-9,516,787-20,713,007-50,303,017-352,121,119

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