Q: What are the factor combinations of the number 500,065,601?

 A:
Positive:   1 x 5000656017 x 71437943241 x 2074961461 x 1084741643 x 7777071687 x 2964233227 x 1549634501 x 111101
Negative: -1 x -500065601-7 x -71437943-241 x -2074961-461 x -1084741-643 x -777707-1687 x -296423-3227 x -154963-4501 x -111101


How do I find the factor combinations of the number 500,065,601?

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 500,065,601, 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.

1 500,065,601
-1 -500,065,601

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 500,065,601.

Example:
1 x 500,065,601 = 500,065,601
and
-1 x -500,065,601 = 500,065,601
Notice both answers equal 500,065,601

With that explanation out of the way, let's continue. Next, we take the number 500,065,601 and divide it by 2:

500,065,601 ÷ 2 = 250,032,800.5

If the quotient is a whole number, then 2 and 250,032,800.5 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:

1 500,065,601
-1 -500,065,601

Now, we try dividing 500,065,601 by 3:

500,065,601 ÷ 3 = 166,688,533.6667

If the quotient is a whole number, then 3 and 166,688,533.6667 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:

1 500,065,601
-1 -500,065,601

Let's try dividing by 4:

500,065,601 ÷ 4 = 125,016,400.25

If the quotient is a whole number, then 4 and 125,016,400.25 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:

1 500,065,601
-1 500,065,601
Keep dividing by the next highest number until you cannot divide anymore.

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

172414616431,6873,2274,501111,101154,963296,423777,7071,084,7412,074,96171,437,943500,065,601
-1-7-241-461-643-1,687-3,227-4,501-111,101-154,963-296,423-777,707-1,084,741-2,074,961-71,437,943-500,065,601

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