Q: What are the factor combinations of the number 723,613,177?

 A:
Positive:   1 x 7236131777 x 10337331117 x 42565481109 x 6638653119 x 6080783763 x 9483791853 x 39050912971 x 55787
Negative: -1 x -723613177-7 x -103373311-17 x -42565481-109 x -6638653-119 x -6080783-763 x -948379-1853 x -390509-12971 x -55787


How do I find the factor combinations of the number 723,613,177?

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 723,613,177, 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.

1 723,613,177
-1 -723,613,177

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 723,613,177.

Example:
1 x 723,613,177 = 723,613,177
and
-1 x -723,613,177 = 723,613,177
Notice both answers equal 723,613,177

With that explanation out of the way, let's continue. Next, we take the number 723,613,177 and divide it by 2:

723,613,177 ÷ 2 = 361,806,588.5

If the quotient is a whole number, then 2 and 361,806,588.5 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:

1 723,613,177
-1 -723,613,177

Now, we try dividing 723,613,177 by 3:

723,613,177 ÷ 3 = 241,204,392.3333

If the quotient is a whole number, then 3 and 241,204,392.3333 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:

1 723,613,177
-1 -723,613,177

Let's try dividing by 4:

723,613,177 ÷ 4 = 180,903,294.25

If the quotient is a whole number, then 4 and 180,903,294.25 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:

1 723,613,177
-1 723,613,177
Keep dividing by the next highest number until you cannot divide anymore.

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

17171091197631,85312,97155,787390,509948,3796,080,7836,638,65342,565,481103,373,311723,613,177
-1-7-17-109-119-763-1,853-12,971-55,787-390,509-948,379-6,080,783-6,638,653-42,565,481-103,373,311-723,613,177

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