Q: What are the factor combinations of the number 352,154,125?

 A:
Positive:   1 x 3521541255 x 7043082525 x 1408616541 x 8589125125 x 2817233205 x 17178251025 x 3435655125 x 68713
Negative: -1 x -352154125-5 x -70430825-25 x -14086165-41 x -8589125-125 x -2817233-205 x -1717825-1025 x -343565-5125 x -68713


How do I find the factor combinations of the number 352,154,125?

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 352,154,125, 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.

1 352,154,125
-1 -352,154,125

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 352,154,125.

Example:
1 x 352,154,125 = 352,154,125
and
-1 x -352,154,125 = 352,154,125
Notice both answers equal 352,154,125

With that explanation out of the way, let's continue. Next, we take the number 352,154,125 and divide it by 2:

352,154,125 ÷ 2 = 176,077,062.5

If the quotient is a whole number, then 2 and 176,077,062.5 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:

1 352,154,125
-1 -352,154,125

Now, we try dividing 352,154,125 by 3:

352,154,125 ÷ 3 = 117,384,708.3333

If the quotient is a whole number, then 3 and 117,384,708.3333 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:

1 352,154,125
-1 -352,154,125

Let's try dividing by 4:

352,154,125 ÷ 4 = 88,038,531.25

If the quotient is a whole number, then 4 and 88,038,531.25 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:

1 352,154,125
-1 352,154,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525411252051,0255,12568,713343,5651,717,8252,817,2338,589,12514,086,16570,430,825352,154,125
-1-5-25-41-125-205-1,025-5,125-68,713-343,565-1,717,825-2,817,233-8,589,125-14,086,165-70,430,825-352,154,125

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