Q: What are the factor combinations of the number 721,435?

 A:
Positive:   1 x 7214355 x 14428711 x 6558513 x 5549555 x 1311765 x 11099143 x 5045715 x 1009
Negative: -1 x -721435-5 x -144287-11 x -65585-13 x -55495-55 x -13117-65 x -11099-143 x -5045-715 x -1009


How do I find the factor combinations of the number 721,435?

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 721,435, 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.

1 721,435
-1 -721,435

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 721,435.

Example:
1 x 721,435 = 721,435
and
-1 x -721,435 = 721,435
Notice both answers equal 721,435

With that explanation out of the way, let's continue. Next, we take the number 721,435 and divide it by 2:

721,435 ÷ 2 = 360,717.5

If the quotient is a whole number, then 2 and 360,717.5 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:

1 721,435
-1 -721,435

Now, we try dividing 721,435 by 3:

721,435 ÷ 3 = 240,478.3333

If the quotient is a whole number, then 3 and 240,478.3333 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:

1 721,435
-1 -721,435

Let's try dividing by 4:

721,435 ÷ 4 = 180,358.75

If the quotient is a whole number, then 4 and 180,358.75 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:

1 721,435
-1 721,435
Keep dividing by the next highest number until you cannot divide anymore.

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

15111355651437151,0095,04511,09913,11755,49565,585144,287721,435
-1-5-11-13-55-65-143-715-1,009-5,045-11,099-13,117-55,495-65,585-144,287-721,435

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 721,435:


Ask a Question