Q: What are the factor combinations of the number 690,944?

 A:
Positive:   1 x 6909442 x 3454724 x 1727368 x 8636816 x 4318432 x 2159264 x 10796128 x 5398256 x 2699
Negative: -1 x -690944-2 x -345472-4 x -172736-8 x -86368-16 x -43184-32 x -21592-64 x -10796-128 x -5398-256 x -2699


How do I find the factor combinations of the number 690,944?

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 690,944, 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.

1 690,944
-1 -690,944

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 690,944.

Example:
1 x 690,944 = 690,944
and
-1 x -690,944 = 690,944
Notice both answers equal 690,944

With that explanation out of the way, let's continue. Next, we take the number 690,944 and divide it by 2:

690,944 ÷ 2 = 345,472

If the quotient is a whole number, then 2 and 345,472 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 2 345,472 690,944
-1 -2 -345,472 -690,944

Now, we try dividing 690,944 by 3:

690,944 ÷ 3 = 230,314.6667

If the quotient is a whole number, then 3 and 230,314.6667 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 2 345,472 690,944
-1 -2 -345,472 -690,944

Let's try dividing by 4:

690,944 ÷ 4 = 172,736

If the quotient is a whole number, then 4 and 172,736 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 4 172,736 345,472 690,944
-1 -2 -4 -172,736 -345,472 690,944
Keep dividing by the next highest number until you cannot divide anymore.

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

12481632641282562,6995,39810,79621,59243,18486,368172,736345,472690,944
-1-2-4-8-16-32-64-128-256-2,699-5,398-10,796-21,592-43,184-86,368-172,736-345,472-690,944

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 690,944:


Ask a Question