Q: What are the factor combinations of the number 500,216,645?

 A:
Positive:   1 x 5002166455 x 100043329211 x 2370695251 x 19928951055 x 4741391255 x 3985791889 x 2648059445 x 52961
Negative: -1 x -500216645-5 x -100043329-211 x -2370695-251 x -1992895-1055 x -474139-1255 x -398579-1889 x -264805-9445 x -52961


How do I find the factor combinations of the number 500,216,645?

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 500,216,645, 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.

1 500,216,645
-1 -500,216,645

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 500,216,645.

Example:
1 x 500,216,645 = 500,216,645
and
-1 x -500,216,645 = 500,216,645
Notice both answers equal 500,216,645

With that explanation out of the way, let's continue. Next, we take the number 500,216,645 and divide it by 2:

500,216,645 ÷ 2 = 250,108,322.5

If the quotient is a whole number, then 2 and 250,108,322.5 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:

1 500,216,645
-1 -500,216,645

Now, we try dividing 500,216,645 by 3:

500,216,645 ÷ 3 = 166,738,881.6667

If the quotient is a whole number, then 3 and 166,738,881.6667 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:

1 500,216,645
-1 -500,216,645

Let's try dividing by 4:

500,216,645 ÷ 4 = 125,054,161.25

If the quotient is a whole number, then 4 and 125,054,161.25 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:

1 500,216,645
-1 500,216,645
Keep dividing by the next highest number until you cannot divide anymore.

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

152112511,0551,2551,8899,44552,961264,805398,579474,1391,992,8952,370,695100,043,329500,216,645
-1-5-211-251-1,055-1,255-1,889-9,445-52,961-264,805-398,579-474,139-1,992,895-2,370,695-100,043,329-500,216,645

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