Q: What are the factor combinations of the number 11,405,021?

 A:
Positive:   1 x 11405021101 x 112921
Negative: -1 x -11405021-101 x -112921


How do I find the factor combinations of the number 11,405,021?

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 11,405,021, 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 11,405,021
-1 -11,405,021

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 11,405,021.

Example:
1 x 11,405,021 = 11,405,021
and
-1 x -11,405,021 = 11,405,021
Notice both answers equal 11,405,021

With that explanation out of the way, let's continue. Next, we take the number 11,405,021 and divide it by 2:

11,405,021 ÷ 2 = 5,702,510.5

If the quotient is a whole number, then 2 and 5,702,510.5 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 11,405,021
-1 -11,405,021

Now, we try dividing 11,405,021 by 3:

11,405,021 ÷ 3 = 3,801,673.6667

If the quotient is a whole number, then 3 and 3,801,673.6667 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 11,405,021
-1 -11,405,021

Let's try dividing by 4:

11,405,021 ÷ 4 = 2,851,255.25

If the quotient is a whole number, then 4 and 2,851,255.25 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 11,405,021
-1 11,405,021
Keep dividing by the next highest number until you cannot divide anymore.

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

1101112,92111,405,021
-1-101-112,921-11,405,021

More Examples

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