Q: What are the factor combinations of the number 333,666?

 A:
Positive:   1 x 3336662 x 1668333 x 1112226 x 556119 x 3707418 x 1853727 x 1235837 x 901854 x 617974 x 4509111 x 3006167 x 1998222 x 1503333 x 1002334 x 999501 x 666
Negative: -1 x -333666-2 x -166833-3 x -111222-6 x -55611-9 x -37074-18 x -18537-27 x -12358-37 x -9018-54 x -6179-74 x -4509-111 x -3006-167 x -1998-222 x -1503-333 x -1002-334 x -999-501 x -666


How do I find the factor combinations of the number 333,666?

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 333,666, 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.

1 333,666
-1 -333,666

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 333,666.

Example:
1 x 333,666 = 333,666
and
-1 x -333,666 = 333,666
Notice both answers equal 333,666

With that explanation out of the way, let's continue. Next, we take the number 333,666 and divide it by 2:

333,666 ÷ 2 = 166,833

If the quotient is a whole number, then 2 and 166,833 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 2 166,833 333,666
-1 -2 -166,833 -333,666

Now, we try dividing 333,666 by 3:

333,666 ÷ 3 = 111,222

If the quotient is a whole number, then 3 and 111,222 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 3 111,222 166,833 333,666
-1 -2 -3 -111,222 -166,833 -333,666

Let's try dividing by 4:

333,666 ÷ 4 = 83,416.5

If the quotient is a whole number, then 4 and 83,416.5 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 2 3 111,222 166,833 333,666
-1 -2 -3 -111,222 -166,833 333,666
Keep dividing by the next highest number until you cannot divide anymore.

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

1236918273754741111672223333345016669991,0021,5031,9983,0064,5096,1799,01812,35818,53737,07455,611111,222166,833333,666
-1-2-3-6-9-18-27-37-54-74-111-167-222-333-334-501-666-999-1,002-1,503-1,998-3,006-4,509-6,179-9,018-12,358-18,537-37,074-55,611-111,222-166,833-333,666

More Examples

Here are some more numbers to try:

333,664333,665333,667333,668
Try the factor calculator

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