Q: What are the factor combinations of the number 729,911?

 A:
Positive:   1 x 7299117 x 10427313 x 5614791 x 8021169 x 4319617 x 1183
Negative: -1 x -729911-7 x -104273-13 x -56147-91 x -8021-169 x -4319-617 x -1183


How do I find the factor combinations of the number 729,911?

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 729,911, 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.

1 729,911
-1 -729,911

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 729,911.

Example:
1 x 729,911 = 729,911
and
-1 x -729,911 = 729,911
Notice both answers equal 729,911

With that explanation out of the way, let's continue. Next, we take the number 729,911 and divide it by 2:

729,911 ÷ 2 = 364,955.5

If the quotient is a whole number, then 2 and 364,955.5 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:

1 729,911
-1 -729,911

Now, we try dividing 729,911 by 3:

729,911 ÷ 3 = 243,303.6667

If the quotient is a whole number, then 3 and 243,303.6667 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:

1 729,911
-1 -729,911

Let's try dividing by 4:

729,911 ÷ 4 = 182,477.75

If the quotient is a whole number, then 4 and 182,477.75 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:

1 729,911
-1 729,911
Keep dividing by the next highest number until you cannot divide anymore.

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

1713911696171,1834,3198,02156,147104,273729,911
-1-7-13-91-169-617-1,183-4,319-8,021-56,147-104,273-729,911

More Examples

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