Q: What are the factor combinations of the number 179,688?

 A:
Positive:   1 x 1796882 x 898443 x 598964 x 449226 x 299488 x 2246112 x 1497424 x 7487
Negative: -1 x -179688-2 x -89844-3 x -59896-4 x -44922-6 x -29948-8 x -22461-12 x -14974-24 x -7487


How do I find the factor combinations of the number 179,688?

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 179,688, 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.

1 179,688
-1 -179,688

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 179,688.

Example:
1 x 179,688 = 179,688
and
-1 x -179,688 = 179,688
Notice both answers equal 179,688

With that explanation out of the way, let's continue. Next, we take the number 179,688 and divide it by 2:

179,688 ÷ 2 = 89,844

If the quotient is a whole number, then 2 and 89,844 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 89,844 179,688
-1 -2 -89,844 -179,688

Now, we try dividing 179,688 by 3:

179,688 ÷ 3 = 59,896

If the quotient is a whole number, then 3 and 59,896 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 59,896 89,844 179,688
-1 -2 -3 -59,896 -89,844 -179,688

Let's try dividing by 4:

179,688 ÷ 4 = 44,922

If the quotient is a whole number, then 4 and 44,922 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 44,922 59,896 89,844 179,688
-1 -2 -3 -4 -44,922 -59,896 -89,844 179,688
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812247,48714,97422,46129,94844,92259,89689,844179,688
-1-2-3-4-6-8-12-24-7,487-14,974-22,461-29,948-44,922-59,896-89,844-179,688

More Examples

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