Q: What are the factor combinations of the number 441,025?

 A:
Positive:   1 x 4410255 x 8820513 x 3392523 x 1917525 x 1764159 x 747565 x 6785115 x 3835295 x 1495299 x 1475325 x 1357575 x 767
Negative: -1 x -441025-5 x -88205-13 x -33925-23 x -19175-25 x -17641-59 x -7475-65 x -6785-115 x -3835-295 x -1495-299 x -1475-325 x -1357-575 x -767


How do I find the factor combinations of the number 441,025?

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 441,025, 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.

1 441,025
-1 -441,025

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 441,025.

Example:
1 x 441,025 = 441,025
and
-1 x -441,025 = 441,025
Notice both answers equal 441,025

With that explanation out of the way, let's continue. Next, we take the number 441,025 and divide it by 2:

441,025 ÷ 2 = 220,512.5

If the quotient is a whole number, then 2 and 220,512.5 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:

1 441,025
-1 -441,025

Now, we try dividing 441,025 by 3:

441,025 ÷ 3 = 147,008.3333

If the quotient is a whole number, then 3 and 147,008.3333 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:

1 441,025
-1 -441,025

Let's try dividing by 4:

441,025 ÷ 4 = 110,256.25

If the quotient is a whole number, then 4 and 110,256.25 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:

1 441,025
-1 441,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1513232559651152952993255757671,3571,4751,4953,8356,7857,47517,64119,17533,92588,205441,025
-1-5-13-23-25-59-65-115-295-299-325-575-767-1,357-1,475-1,495-3,835-6,785-7,475-17,641-19,175-33,925-88,205-441,025

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