Q: What are the factor combinations of the number 404,243?

 A:
Positive:   1 x 4042437 x 5774917 x 2377943 x 940179 x 5117119 x 3397301 x 1343553 x 731
Negative: -1 x -404243-7 x -57749-17 x -23779-43 x -9401-79 x -5117-119 x -3397-301 x -1343-553 x -731


How do I find the factor combinations of the number 404,243?

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 404,243, 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.

1 404,243
-1 -404,243

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 404,243.

Example:
1 x 404,243 = 404,243
and
-1 x -404,243 = 404,243
Notice both answers equal 404,243

With that explanation out of the way, let's continue. Next, we take the number 404,243 and divide it by 2:

404,243 ÷ 2 = 202,121.5

If the quotient is a whole number, then 2 and 202,121.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 404,243
-1 -404,243

Now, we try dividing 404,243 by 3:

404,243 ÷ 3 = 134,747.6667

If the quotient is a whole number, then 3 and 134,747.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 404,243
-1 -404,243

Let's try dividing by 4:

404,243 ÷ 4 = 101,060.75

If the quotient is a whole number, then 4 and 101,060.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 404,243
-1 404,243
Keep dividing by the next highest number until you cannot divide anymore.

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

171743791193015537311,3433,3975,1179,40123,77957,749404,243
-1-7-17-43-79-119-301-553-731-1,343-3,397-5,117-9,401-23,779-57,749-404,243

More Examples

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