Q: What are the factor combinations of the number 724,308,625?

 A:
Positive:   1 x 7243086255 x 14486172525 x 28972345125 x 5794469
Negative: -1 x -724308625-5 x -144861725-25 x -28972345-125 x -5794469


How do I find the factor combinations of the number 724,308,625?

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 724,308,625, 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.

1 724,308,625
-1 -724,308,625

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 724,308,625.

Example:
1 x 724,308,625 = 724,308,625
and
-1 x -724,308,625 = 724,308,625
Notice both answers equal 724,308,625

With that explanation out of the way, let's continue. Next, we take the number 724,308,625 and divide it by 2:

724,308,625 ÷ 2 = 362,154,312.5

If the quotient is a whole number, then 2 and 362,154,312.5 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:

1 724,308,625
-1 -724,308,625

Now, we try dividing 724,308,625 by 3:

724,308,625 ÷ 3 = 241,436,208.3333

If the quotient is a whole number, then 3 and 241,436,208.3333 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:

1 724,308,625
-1 -724,308,625

Let's try dividing by 4:

724,308,625 ÷ 4 = 181,077,156.25

If the quotient is a whole number, then 4 and 181,077,156.25 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:

1 724,308,625
-1 724,308,625
Keep dividing by the next highest number until you cannot divide anymore.

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

15251255,794,46928,972,345144,861,725724,308,625
-1-5-25-125-5,794,469-28,972,345-144,861,725-724,308,625

More Examples

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