Q: What are the factor combinations of the number 104,406,012?

 A:
Positive:   1 x 1044060122 x 522030063 x 348020044 x 261015036 x 174010029 x 1160066812 x 870050118 x 580033436 x 2900167
Negative: -1 x -104406012-2 x -52203006-3 x -34802004-4 x -26101503-6 x -17401002-9 x -11600668-12 x -8700501-18 x -5800334-36 x -2900167


How do I find the factor combinations of the number 104,406,012?

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 104,406,012, 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.

1 104,406,012
-1 -104,406,012

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 104,406,012.

Example:
1 x 104,406,012 = 104,406,012
and
-1 x -104,406,012 = 104,406,012
Notice both answers equal 104,406,012

With that explanation out of the way, let's continue. Next, we take the number 104,406,012 and divide it by 2:

104,406,012 ÷ 2 = 52,203,006

If the quotient is a whole number, then 2 and 52,203,006 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 52,203,006 104,406,012
-1 -2 -52,203,006 -104,406,012

Now, we try dividing 104,406,012 by 3:

104,406,012 ÷ 3 = 34,802,004

If the quotient is a whole number, then 3 and 34,802,004 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 34,802,004 52,203,006 104,406,012
-1 -2 -3 -34,802,004 -52,203,006 -104,406,012

Let's try dividing by 4:

104,406,012 ÷ 4 = 26,101,503

If the quotient is a whole number, then 4 and 26,101,503 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 26,101,503 34,802,004 52,203,006 104,406,012
-1 -2 -3 -4 -26,101,503 -34,802,004 -52,203,006 104,406,012
Keep dividing by the next highest number until you cannot divide anymore.

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

1234691218362,900,1675,800,3348,700,50111,600,66817,401,00226,101,50334,802,00452,203,006104,406,012
-1-2-3-4-6-9-12-18-36-2,900,167-5,800,334-8,700,501-11,600,668-17,401,002-26,101,503-34,802,004-52,203,006-104,406,012

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