Q: What are the factor combinations of the number 106,022,665?

 A:
Positive:   1 x 1060226655 x 212045337 x 1514609535 x 3029219109 x 972685545 x 194537763 x 1389553815 x 27791
Negative: -1 x -106022665-5 x -21204533-7 x -15146095-35 x -3029219-109 x -972685-545 x -194537-763 x -138955-3815 x -27791


How do I find the factor combinations of the number 106,022,665?

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 106,022,665, 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.

1 106,022,665
-1 -106,022,665

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 106,022,665.

Example:
1 x 106,022,665 = 106,022,665
and
-1 x -106,022,665 = 106,022,665
Notice both answers equal 106,022,665

With that explanation out of the way, let's continue. Next, we take the number 106,022,665 and divide it by 2:

106,022,665 ÷ 2 = 53,011,332.5

If the quotient is a whole number, then 2 and 53,011,332.5 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:

1 106,022,665
-1 -106,022,665

Now, we try dividing 106,022,665 by 3:

106,022,665 ÷ 3 = 35,340,888.3333

If the quotient is a whole number, then 3 and 35,340,888.3333 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:

1 106,022,665
-1 -106,022,665

Let's try dividing by 4:

106,022,665 ÷ 4 = 26,505,666.25

If the quotient is a whole number, then 4 and 26,505,666.25 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:

1 106,022,665
-1 106,022,665
Keep dividing by the next highest number until you cannot divide anymore.

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

157351095457633,81527,791138,955194,537972,6853,029,21915,146,09521,204,533106,022,665
-1-5-7-35-109-545-763-3,815-27,791-138,955-194,537-972,685-3,029,219-15,146,095-21,204,533-106,022,665

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