Q: What are the factor combinations of the number 690,996?

 A:
Positive:   1 x 6909962 x 3454983 x 2303324 x 1727496 x 11516612 x 5758389 x 7764178 x 3882267 x 2588356 x 1941534 x 1294647 x 1068
Negative: -1 x -690996-2 x -345498-3 x -230332-4 x -172749-6 x -115166-12 x -57583-89 x -7764-178 x -3882-267 x -2588-356 x -1941-534 x -1294-647 x -1068


How do I find the factor combinations of the number 690,996?

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 690,996, 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.

1 690,996
-1 -690,996

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 690,996.

Example:
1 x 690,996 = 690,996
and
-1 x -690,996 = 690,996
Notice both answers equal 690,996

With that explanation out of the way, let's continue. Next, we take the number 690,996 and divide it by 2:

690,996 ÷ 2 = 345,498

If the quotient is a whole number, then 2 and 345,498 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 2 345,498 690,996
-1 -2 -345,498 -690,996

Now, we try dividing 690,996 by 3:

690,996 ÷ 3 = 230,332

If the quotient is a whole number, then 3 and 230,332 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 3 230,332 345,498 690,996
-1 -2 -3 -230,332 -345,498 -690,996

Let's try dividing by 4:

690,996 ÷ 4 = 172,749

If the quotient is a whole number, then 4 and 172,749 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 4 172,749 230,332 345,498 690,996
-1 -2 -3 -4 -172,749 -230,332 -345,498 690,996
Keep dividing by the next highest number until you cannot divide anymore.

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

1234612891782673565346471,0681,2941,9412,5883,8827,76457,583115,166172,749230,332345,498690,996
-1-2-3-4-6-12-89-178-267-356-534-647-1,068-1,294-1,941-2,588-3,882-7,764-57,583-115,166-172,749-230,332-345,498-690,996

More Examples

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