Q: What are the factor combinations of the number 404,225?

 A:
Positive:   1 x 4042255 x 8084519 x 2127523 x 1757525 x 1616937 x 1092595 x 4255115 x 3515185 x 2185437 x 925475 x 851575 x 703
Negative: -1 x -404225-5 x -80845-19 x -21275-23 x -17575-25 x -16169-37 x -10925-95 x -4255-115 x -3515-185 x -2185-437 x -925-475 x -851-575 x -703


How do I find the factor combinations of the number 404,225?

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 404,225, 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.

1 404,225
-1 -404,225

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 404,225.

Example:
1 x 404,225 = 404,225
and
-1 x -404,225 = 404,225
Notice both answers equal 404,225

With that explanation out of the way, let's continue. Next, we take the number 404,225 and divide it by 2:

404,225 ÷ 2 = 202,112.5

If the quotient is a whole number, then 2 and 202,112.5 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:

1 404,225
-1 -404,225

Now, we try dividing 404,225 by 3:

404,225 ÷ 3 = 134,741.6667

If the quotient is a whole number, then 3 and 134,741.6667 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:

1 404,225
-1 -404,225

Let's try dividing by 4:

404,225 ÷ 4 = 101,056.25

If the quotient is a whole number, then 4 and 101,056.25 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:

1 404,225
-1 404,225
Keep dividing by the next highest number until you cannot divide anymore.

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

1519232537951151854374755757038519252,1853,5154,25510,92516,16917,57521,27580,845404,225
-1-5-19-23-25-37-95-115-185-437-475-575-703-851-925-2,185-3,515-4,255-10,925-16,169-17,575-21,275-80,845-404,225

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