Q: What are the factor combinations of the number 666,945?

 A:
Positive:   1 x 6669453 x 2223155 x 1333899 x 7410515 x 4446345 x 14821
Negative: -1 x -666945-3 x -222315-5 x -133389-9 x -74105-15 x -44463-45 x -14821


How do I find the factor combinations of the number 666,945?

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 666,945, 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.

1 666,945
-1 -666,945

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 666,945.

Example:
1 x 666,945 = 666,945
and
-1 x -666,945 = 666,945
Notice both answers equal 666,945

With that explanation out of the way, let's continue. Next, we take the number 666,945 and divide it by 2:

666,945 ÷ 2 = 333,472.5

If the quotient is a whole number, then 2 and 333,472.5 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:

1 666,945
-1 -666,945

Now, we try dividing 666,945 by 3:

666,945 ÷ 3 = 222,315

If the quotient is a whole number, then 3 and 222,315 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 3 222,315 666,945
-1 -3 -222,315 -666,945

Let's try dividing by 4:

666,945 ÷ 4 = 166,736.25

If the quotient is a whole number, then 4 and 166,736.25 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 3 222,315 666,945
-1 -3 -222,315 666,945
Keep dividing by the next highest number until you cannot divide anymore.

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

1359154514,82144,46374,105133,389222,315666,945
-1-3-5-9-15-45-14,821-44,463-74,105-133,389-222,315-666,945

More Examples

Here are some more numbers to try:

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