Q: What are the factor combinations of the number 533,748?

 A:
Positive:   1 x 5337482 x 2668743 x 1779164 x 1334376 x 8895812 x 4447919 x 2809238 x 1404657 x 936476 x 7023114 x 4682228 x 2341
Negative: -1 x -533748-2 x -266874-3 x -177916-4 x -133437-6 x -88958-12 x -44479-19 x -28092-38 x -14046-57 x -9364-76 x -7023-114 x -4682-228 x -2341


How do I find the factor combinations of the number 533,748?

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 533,748, 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.

1 533,748
-1 -533,748

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 533,748.

Example:
1 x 533,748 = 533,748
and
-1 x -533,748 = 533,748
Notice both answers equal 533,748

With that explanation out of the way, let's continue. Next, we take the number 533,748 and divide it by 2:

533,748 ÷ 2 = 266,874

If the quotient is a whole number, then 2 and 266,874 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 2 266,874 533,748
-1 -2 -266,874 -533,748

Now, we try dividing 533,748 by 3:

533,748 ÷ 3 = 177,916

If the quotient is a whole number, then 3 and 177,916 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 3 177,916 266,874 533,748
-1 -2 -3 -177,916 -266,874 -533,748

Let's try dividing by 4:

533,748 ÷ 4 = 133,437

If the quotient is a whole number, then 4 and 133,437 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 4 133,437 177,916 266,874 533,748
-1 -2 -3 -4 -133,437 -177,916 -266,874 533,748
Keep dividing by the next highest number until you cannot divide anymore.

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

1234612193857761142282,3414,6827,0239,36414,04628,09244,47988,958133,437177,916266,874533,748
-1-2-3-4-6-12-19-38-57-76-114-228-2,341-4,682-7,023-9,364-14,046-28,092-44,479-88,958-133,437-177,916-266,874-533,748

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