Q: What are the factor combinations of the number 353,604,461?

 A:
Positive:   1 x 3536044617 x 5051492323 x 15374107161 x 2196301467 x 7571833269 x 1081694703 x 7518710741 x 32921
Negative: -1 x -353604461-7 x -50514923-23 x -15374107-161 x -2196301-467 x -757183-3269 x -108169-4703 x -75187-10741 x -32921


How do I find the factor combinations of the number 353,604,461?

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 353,604,461, 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.

1 353,604,461
-1 -353,604,461

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 353,604,461.

Example:
1 x 353,604,461 = 353,604,461
and
-1 x -353,604,461 = 353,604,461
Notice both answers equal 353,604,461

With that explanation out of the way, let's continue. Next, we take the number 353,604,461 and divide it by 2:

353,604,461 ÷ 2 = 176,802,230.5

If the quotient is a whole number, then 2 and 176,802,230.5 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:

1 353,604,461
-1 -353,604,461

Now, we try dividing 353,604,461 by 3:

353,604,461 ÷ 3 = 117,868,153.6667

If the quotient is a whole number, then 3 and 117,868,153.6667 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:

1 353,604,461
-1 -353,604,461

Let's try dividing by 4:

353,604,461 ÷ 4 = 88,401,115.25

If the quotient is a whole number, then 4 and 88,401,115.25 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:

1 353,604,461
-1 353,604,461
Keep dividing by the next highest number until you cannot divide anymore.

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

17231614673,2694,70310,74132,92175,187108,169757,1832,196,30115,374,10750,514,923353,604,461
-1-7-23-161-467-3,269-4,703-10,741-32,921-75,187-108,169-757,183-2,196,301-15,374,107-50,514,923-353,604,461

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