Q: What are the factor combinations of the number 666,721,816?

 A:
Positive:   1 x 6667218162 x 3333609084 x 1666804548 x 83340227997 x 6687281994 x 3343643988 x 1671827976 x 83591
Negative: -1 x -666721816-2 x -333360908-4 x -166680454-8 x -83340227-997 x -668728-1994 x -334364-3988 x -167182-7976 x -83591


How do I find the factor combinations of the number 666,721,816?

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 666,721,816, 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.

1 666,721,816
-1 -666,721,816

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 666,721,816.

Example:
1 x 666,721,816 = 666,721,816
and
-1 x -666,721,816 = 666,721,816
Notice both answers equal 666,721,816

With that explanation out of the way, let's continue. Next, we take the number 666,721,816 and divide it by 2:

666,721,816 ÷ 2 = 333,360,908

If the quotient is a whole number, then 2 and 333,360,908 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 333,360,908 666,721,816
-1 -2 -333,360,908 -666,721,816

Now, we try dividing 666,721,816 by 3:

666,721,816 ÷ 3 = 222,240,605.3333

If the quotient is a whole number, then 3 and 222,240,605.3333 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 2 333,360,908 666,721,816
-1 -2 -333,360,908 -666,721,816

Let's try dividing by 4:

666,721,816 ÷ 4 = 166,680,454

If the quotient is a whole number, then 4 and 166,680,454 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 166,680,454 333,360,908 666,721,816
-1 -2 -4 -166,680,454 -333,360,908 666,721,816
Keep dividing by the next highest number until you cannot divide anymore.

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

12489971,9943,9887,97683,591167,182334,364668,72883,340,227166,680,454333,360,908666,721,816
-1-2-4-8-997-1,994-3,988-7,976-83,591-167,182-334,364-668,728-83,340,227-166,680,454-333,360,908-666,721,816

More Examples

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