Q: What are the factor combinations of the number 666,746,729?

 A:
Positive:   1 x 66674672911 x 6061333931 x 2150795971 x 9390799341 x 1955269781 x 8537092201 x 30292924211 x 27539
Negative: -1 x -666746729-11 x -60613339-31 x -21507959-71 x -9390799-341 x -1955269-781 x -853709-2201 x -302929-24211 x -27539


How do I find the factor combinations of the number 666,746,729?

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 666,746,729, 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.

1 666,746,729
-1 -666,746,729

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 666,746,729.

Example:
1 x 666,746,729 = 666,746,729
and
-1 x -666,746,729 = 666,746,729
Notice both answers equal 666,746,729

With that explanation out of the way, let's continue. Next, we take the number 666,746,729 and divide it by 2:

666,746,729 ÷ 2 = 333,373,364.5

If the quotient is a whole number, then 2 and 333,373,364.5 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:

1 666,746,729
-1 -666,746,729

Now, we try dividing 666,746,729 by 3:

666,746,729 ÷ 3 = 222,248,909.6667

If the quotient is a whole number, then 3 and 222,248,909.6667 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:

1 666,746,729
-1 -666,746,729

Let's try dividing by 4:

666,746,729 ÷ 4 = 166,686,682.25

If the quotient is a whole number, then 4 and 166,686,682.25 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:

1 666,746,729
-1 666,746,729
Keep dividing by the next highest number until you cannot divide anymore.

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

11131713417812,20124,21127,539302,929853,7091,955,2699,390,79921,507,95960,613,339666,746,729
-1-11-31-71-341-781-2,201-24,211-27,539-302,929-853,709-1,955,269-9,390,799-21,507,959-60,613,339-666,746,729

More Examples

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