Q: What are the factor combinations of the number 721,412,623?

 A:
Positive:   1 x 72141262314717 x 49019
Negative: -1 x -721412623-14717 x -49019


How do I find the factor combinations of the number 721,412,623?

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 721,412,623, 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.

1 721,412,623
-1 -721,412,623

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 721,412,623.

Example:
1 x 721,412,623 = 721,412,623
and
-1 x -721,412,623 = 721,412,623
Notice both answers equal 721,412,623

With that explanation out of the way, let's continue. Next, we take the number 721,412,623 and divide it by 2:

721,412,623 ÷ 2 = 360,706,311.5

If the quotient is a whole number, then 2 and 360,706,311.5 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:

1 721,412,623
-1 -721,412,623

Now, we try dividing 721,412,623 by 3:

721,412,623 ÷ 3 = 240,470,874.3333

If the quotient is a whole number, then 3 and 240,470,874.3333 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:

1 721,412,623
-1 -721,412,623

Let's try dividing by 4:

721,412,623 ÷ 4 = 180,353,155.75

If the quotient is a whole number, then 4 and 180,353,155.75 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:

1 721,412,623
-1 721,412,623
Keep dividing by the next highest number until you cannot divide anymore.

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

114,71749,019721,412,623
-1-14,717-49,019-721,412,623

More Examples

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