Q: What are the factor combinations of the number 224,000,405?

 A:
Positive:   1 x 2240004055 x 4480008119 x 1178949537 x 605406595 x 2357899185 x 1210813703 x 3186353515 x 63727
Negative: -1 x -224000405-5 x -44800081-19 x -11789495-37 x -6054065-95 x -2357899-185 x -1210813-703 x -318635-3515 x -63727


How do I find the factor combinations of the number 224,000,405?

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 224,000,405, 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.

1 224,000,405
-1 -224,000,405

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 224,000,405.

Example:
1 x 224,000,405 = 224,000,405
and
-1 x -224,000,405 = 224,000,405
Notice both answers equal 224,000,405

With that explanation out of the way, let's continue. Next, we take the number 224,000,405 and divide it by 2:

224,000,405 ÷ 2 = 112,000,202.5

If the quotient is a whole number, then 2 and 112,000,202.5 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:

1 224,000,405
-1 -224,000,405

Now, we try dividing 224,000,405 by 3:

224,000,405 ÷ 3 = 74,666,801.6667

If the quotient is a whole number, then 3 and 74,666,801.6667 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:

1 224,000,405
-1 -224,000,405

Let's try dividing by 4:

224,000,405 ÷ 4 = 56,000,101.25

If the quotient is a whole number, then 4 and 56,000,101.25 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:

1 224,000,405
-1 224,000,405
Keep dividing by the next highest number until you cannot divide anymore.

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

151937951857033,51563,727318,6351,210,8132,357,8996,054,06511,789,49544,800,081224,000,405
-1-5-19-37-95-185-703-3,515-63,727-318,635-1,210,813-2,357,899-6,054,065-11,789,495-44,800,081-224,000,405

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