Q: What are the factor combinations of the number 720,382,169?

 A:
Positive:   1 x 72038216913 x 5541401319 x 37914851247 x 2916527
Negative: -1 x -720382169-13 x -55414013-19 x -37914851-247 x -2916527


How do I find the factor combinations of the number 720,382,169?

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 720,382,169, 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.

1 720,382,169
-1 -720,382,169

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 720,382,169.

Example:
1 x 720,382,169 = 720,382,169
and
-1 x -720,382,169 = 720,382,169
Notice both answers equal 720,382,169

With that explanation out of the way, let's continue. Next, we take the number 720,382,169 and divide it by 2:

720,382,169 ÷ 2 = 360,191,084.5

If the quotient is a whole number, then 2 and 360,191,084.5 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:

1 720,382,169
-1 -720,382,169

Now, we try dividing 720,382,169 by 3:

720,382,169 ÷ 3 = 240,127,389.6667

If the quotient is a whole number, then 3 and 240,127,389.6667 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:

1 720,382,169
-1 -720,382,169

Let's try dividing by 4:

720,382,169 ÷ 4 = 180,095,542.25

If the quotient is a whole number, then 4 and 180,095,542.25 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:

1 720,382,169
-1 720,382,169
Keep dividing by the next highest number until you cannot divide anymore.

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

113192472,916,52737,914,85155,414,013720,382,169
-1-13-19-247-2,916,527-37,914,851-55,414,013-720,382,169

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