Q: What are the factor combinations of the number 144,311,405?

 A:
Positive:   1 x 1443114055 x 288622817 x 2061591535 x 412318371 x 2032555355 x 406511497 x 2903652485 x 58073
Negative: -1 x -144311405-5 x -28862281-7 x -20615915-35 x -4123183-71 x -2032555-355 x -406511-497 x -290365-2485 x -58073


How do I find the factor combinations of the number 144,311,405?

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 144,311,405, 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.

1 144,311,405
-1 -144,311,405

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 144,311,405.

Example:
1 x 144,311,405 = 144,311,405
and
-1 x -144,311,405 = 144,311,405
Notice both answers equal 144,311,405

With that explanation out of the way, let's continue. Next, we take the number 144,311,405 and divide it by 2:

144,311,405 ÷ 2 = 72,155,702.5

If the quotient is a whole number, then 2 and 72,155,702.5 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:

1 144,311,405
-1 -144,311,405

Now, we try dividing 144,311,405 by 3:

144,311,405 ÷ 3 = 48,103,801.6667

If the quotient is a whole number, then 3 and 48,103,801.6667 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:

1 144,311,405
-1 -144,311,405

Let's try dividing by 4:

144,311,405 ÷ 4 = 36,077,851.25

If the quotient is a whole number, then 4 and 36,077,851.25 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:

1 144,311,405
-1 144,311,405
Keep dividing by the next highest number until you cannot divide anymore.

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

15735713554972,48558,073290,365406,5112,032,5554,123,18320,615,91528,862,281144,311,405
-1-5-7-35-71-355-497-2,485-58,073-290,365-406,511-2,032,555-4,123,183-20,615,915-28,862,281-144,311,405

More Examples

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