Q: What are the factor combinations of the number 726,134,537?

 A:
Positive:   1 x 72613453747 x 1544967171 x 10227247167 x 43481111303 x 5572793337 x 2176017849 x 9251311857 x 61241
Negative: -1 x -726134537-47 x -15449671-71 x -10227247-167 x -4348111-1303 x -557279-3337 x -217601-7849 x -92513-11857 x -61241


How do I find the factor combinations of the number 726,134,537?

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 726,134,537, 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.

1 726,134,537
-1 -726,134,537

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 726,134,537.

Example:
1 x 726,134,537 = 726,134,537
and
-1 x -726,134,537 = 726,134,537
Notice both answers equal 726,134,537

With that explanation out of the way, let's continue. Next, we take the number 726,134,537 and divide it by 2:

726,134,537 ÷ 2 = 363,067,268.5

If the quotient is a whole number, then 2 and 363,067,268.5 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:

1 726,134,537
-1 -726,134,537

Now, we try dividing 726,134,537 by 3:

726,134,537 ÷ 3 = 242,044,845.6667

If the quotient is a whole number, then 3 and 242,044,845.6667 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:

1 726,134,537
-1 -726,134,537

Let's try dividing by 4:

726,134,537 ÷ 4 = 181,533,634.25

If the quotient is a whole number, then 4 and 181,533,634.25 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:

1 726,134,537
-1 726,134,537
Keep dividing by the next highest number until you cannot divide anymore.

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

147711671,3033,3377,84911,85761,24192,513217,601557,2794,348,11110,227,24715,449,671726,134,537
-1-47-71-167-1,303-3,337-7,849-11,857-61,241-92,513-217,601-557,279-4,348,111-10,227,247-15,449,671-726,134,537

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