Q: What are the factor combinations of the number 690,192?

 A:
Positive:   1 x 6901922 x 3450963 x 2300644 x 1725486 x 1150328 x 862749 x 7668812 x 5751616 x 4313718 x 3834424 x 2875836 x 1917248 x 1437972 x 9586144 x 4793
Negative: -1 x -690192-2 x -345096-3 x -230064-4 x -172548-6 x -115032-8 x -86274-9 x -76688-12 x -57516-16 x -43137-18 x -38344-24 x -28758-36 x -19172-48 x -14379-72 x -9586-144 x -4793


How do I find the factor combinations of the number 690,192?

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 690,192, 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.

1 690,192
-1 -690,192

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 690,192.

Example:
1 x 690,192 = 690,192
and
-1 x -690,192 = 690,192
Notice both answers equal 690,192

With that explanation out of the way, let's continue. Next, we take the number 690,192 and divide it by 2:

690,192 ÷ 2 = 345,096

If the quotient is a whole number, then 2 and 345,096 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 2 345,096 690,192
-1 -2 -345,096 -690,192

Now, we try dividing 690,192 by 3:

690,192 ÷ 3 = 230,064

If the quotient is a whole number, then 3 and 230,064 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 3 230,064 345,096 690,192
-1 -2 -3 -230,064 -345,096 -690,192

Let's try dividing by 4:

690,192 ÷ 4 = 172,548

If the quotient is a whole number, then 4 and 172,548 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 4 172,548 230,064 345,096 690,192
-1 -2 -3 -4 -172,548 -230,064 -345,096 690,192
Keep dividing by the next highest number until you cannot divide anymore.

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

1234689121618243648721444,7939,58614,37919,17228,75838,34443,13757,51676,68886,274115,032172,548230,064345,096690,192
-1-2-3-4-6-8-9-12-16-18-24-36-48-72-144-4,793-9,586-14,379-19,172-28,758-38,344-43,137-57,516-76,688-86,274-115,032-172,548-230,064-345,096-690,192

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