Q: What are the factor combinations of the number 527,484?

 A:
Positive:   1 x 5274842 x 2637423 x 1758284 x 1318716 x 8791412 x 43957113 x 4668226 x 2334339 x 1556389 x 1356452 x 1167678 x 778
Negative: -1 x -527484-2 x -263742-3 x -175828-4 x -131871-6 x -87914-12 x -43957-113 x -4668-226 x -2334-339 x -1556-389 x -1356-452 x -1167-678 x -778


How do I find the factor combinations of the number 527,484?

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 527,484, 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.

1 527,484
-1 -527,484

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 527,484.

Example:
1 x 527,484 = 527,484
and
-1 x -527,484 = 527,484
Notice both answers equal 527,484

With that explanation out of the way, let's continue. Next, we take the number 527,484 and divide it by 2:

527,484 ÷ 2 = 263,742

If the quotient is a whole number, then 2 and 263,742 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 2 263,742 527,484
-1 -2 -263,742 -527,484

Now, we try dividing 527,484 by 3:

527,484 ÷ 3 = 175,828

If the quotient is a whole number, then 3 and 175,828 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 3 175,828 263,742 527,484
-1 -2 -3 -175,828 -263,742 -527,484

Let's try dividing by 4:

527,484 ÷ 4 = 131,871

If the quotient is a whole number, then 4 and 131,871 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 4 131,871 175,828 263,742 527,484
-1 -2 -3 -4 -131,871 -175,828 -263,742 527,484
Keep dividing by the next highest number until you cannot divide anymore.

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

12346121132263393894526787781,1671,3561,5562,3344,66843,95787,914131,871175,828263,742527,484
-1-2-3-4-6-12-113-226-339-389-452-678-778-1,167-1,356-1,556-2,334-4,668-43,957-87,914-131,871-175,828-263,742-527,484

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