Q: What are the factor combinations of the number 352,412,567?

 A:
Positive:   1 x 35241256713 x 2710865917 x 20730151221 x 1594627523 x 6738293049 x 1155836799 x 518338891 x 39637
Negative: -1 x -352412567-13 x -27108659-17 x -20730151-221 x -1594627-523 x -673829-3049 x -115583-6799 x -51833-8891 x -39637


How do I find the factor combinations of the number 352,412,567?

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 352,412,567, 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.

1 352,412,567
-1 -352,412,567

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 352,412,567.

Example:
1 x 352,412,567 = 352,412,567
and
-1 x -352,412,567 = 352,412,567
Notice both answers equal 352,412,567

With that explanation out of the way, let's continue. Next, we take the number 352,412,567 and divide it by 2:

352,412,567 ÷ 2 = 176,206,283.5

If the quotient is a whole number, then 2 and 176,206,283.5 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:

1 352,412,567
-1 -352,412,567

Now, we try dividing 352,412,567 by 3:

352,412,567 ÷ 3 = 117,470,855.6667

If the quotient is a whole number, then 3 and 117,470,855.6667 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:

1 352,412,567
-1 -352,412,567

Let's try dividing by 4:

352,412,567 ÷ 4 = 88,103,141.75

If the quotient is a whole number, then 4 and 88,103,141.75 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:

1 352,412,567
-1 352,412,567
Keep dividing by the next highest number until you cannot divide anymore.

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

113172215233,0496,7998,89139,63751,833115,583673,8291,594,62720,730,15127,108,659352,412,567
-1-13-17-221-523-3,049-6,799-8,891-39,637-51,833-115,583-673,829-1,594,627-20,730,151-27,108,659-352,412,567

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