Q: What are the factor combinations of the number 726,636,661?

 A:
Positive:   1 x 72663666117 x 4274333343 x 16898527731 x 9940311849 x 39298923117 x 31433
Negative: -1 x -726636661-17 x -42743333-43 x -16898527-731 x -994031-1849 x -392989-23117 x -31433


How do I find the factor combinations of the number 726,636,661?

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 726,636,661, 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.

1 726,636,661
-1 -726,636,661

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 726,636,661.

Example:
1 x 726,636,661 = 726,636,661
and
-1 x -726,636,661 = 726,636,661
Notice both answers equal 726,636,661

With that explanation out of the way, let's continue. Next, we take the number 726,636,661 and divide it by 2:

726,636,661 ÷ 2 = 363,318,330.5

If the quotient is a whole number, then 2 and 363,318,330.5 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:

1 726,636,661
-1 -726,636,661

Now, we try dividing 726,636,661 by 3:

726,636,661 ÷ 3 = 242,212,220.3333

If the quotient is a whole number, then 3 and 242,212,220.3333 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:

1 726,636,661
-1 -726,636,661

Let's try dividing by 4:

726,636,661 ÷ 4 = 181,659,165.25

If the quotient is a whole number, then 4 and 181,659,165.25 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:

1 726,636,661
-1 726,636,661
Keep dividing by the next highest number until you cannot divide anymore.

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

117437311,84923,11731,433392,989994,03116,898,52742,743,333726,636,661
-1-17-43-731-1,849-23,117-31,433-392,989-994,031-16,898,527-42,743,333-726,636,661

More Examples

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