Q: What are the factor combinations of the number 106,056,508?

 A:
Positive:   1 x 1060565082 x 530282544 x 26514127
Negative: -1 x -106056508-2 x -53028254-4 x -26514127


How do I find the factor combinations of the number 106,056,508?

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 106,056,508, 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.

1 106,056,508
-1 -106,056,508

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 106,056,508.

Example:
1 x 106,056,508 = 106,056,508
and
-1 x -106,056,508 = 106,056,508
Notice both answers equal 106,056,508

With that explanation out of the way, let's continue. Next, we take the number 106,056,508 and divide it by 2:

106,056,508 ÷ 2 = 53,028,254

If the quotient is a whole number, then 2 and 53,028,254 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 53,028,254 106,056,508
-1 -2 -53,028,254 -106,056,508

Now, we try dividing 106,056,508 by 3:

106,056,508 ÷ 3 = 35,352,169.3333

If the quotient is a whole number, then 3 and 35,352,169.3333 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 2 53,028,254 106,056,508
-1 -2 -53,028,254 -106,056,508

Let's try dividing by 4:

106,056,508 ÷ 4 = 26,514,127

If the quotient is a whole number, then 4 and 26,514,127 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 4 26,514,127 53,028,254 106,056,508
-1 -2 -4 -26,514,127 -53,028,254 106,056,508
Keep dividing by the next highest number until you cannot divide anymore.

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

12426,514,12753,028,254106,056,508
-1-2-4-26,514,127-53,028,254-106,056,508

More Examples

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