Q: What are the factor combinations of the number 736,968?

 A:
Positive:   1 x 7369682 x 3684843 x 2456564 x 1842426 x 1228288 x 9212112 x 6141424 x 30707
Negative: -1 x -736968-2 x -368484-3 x -245656-4 x -184242-6 x -122828-8 x -92121-12 x -61414-24 x -30707


How do I find the factor combinations of the number 736,968?

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 736,968, 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.

1 736,968
-1 -736,968

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 736,968.

Example:
1 x 736,968 = 736,968
and
-1 x -736,968 = 736,968
Notice both answers equal 736,968

With that explanation out of the way, let's continue. Next, we take the number 736,968 and divide it by 2:

736,968 ÷ 2 = 368,484

If the quotient is a whole number, then 2 and 368,484 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 2 368,484 736,968
-1 -2 -368,484 -736,968

Now, we try dividing 736,968 by 3:

736,968 ÷ 3 = 245,656

If the quotient is a whole number, then 3 and 245,656 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 3 245,656 368,484 736,968
-1 -2 -3 -245,656 -368,484 -736,968

Let's try dividing by 4:

736,968 ÷ 4 = 184,242

If the quotient is a whole number, then 4 and 184,242 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 4 184,242 245,656 368,484 736,968
-1 -2 -3 -4 -184,242 -245,656 -368,484 736,968
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122430,70761,41492,121122,828184,242245,656368,484736,968
-1-2-3-4-6-8-12-24-30,707-61,414-92,121-122,828-184,242-245,656-368,484-736,968

More Examples

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