Q: What are the factor combinations of the number 663,425?

 A:
Positive:   1 x 6634255 x 1326857 x 9477517 x 3902525 x 2653735 x 1895585 x 7805119 x 5575175 x 3791223 x 2975425 x 1561595 x 1115
Negative: -1 x -663425-5 x -132685-7 x -94775-17 x -39025-25 x -26537-35 x -18955-85 x -7805-119 x -5575-175 x -3791-223 x -2975-425 x -1561-595 x -1115


How do I find the factor combinations of the number 663,425?

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 663,425, 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.

1 663,425
-1 -663,425

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 663,425.

Example:
1 x 663,425 = 663,425
and
-1 x -663,425 = 663,425
Notice both answers equal 663,425

With that explanation out of the way, let's continue. Next, we take the number 663,425 and divide it by 2:

663,425 ÷ 2 = 331,712.5

If the quotient is a whole number, then 2 and 331,712.5 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:

1 663,425
-1 -663,425

Now, we try dividing 663,425 by 3:

663,425 ÷ 3 = 221,141.6667

If the quotient is a whole number, then 3 and 221,141.6667 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:

1 663,425
-1 -663,425

Let's try dividing by 4:

663,425 ÷ 4 = 165,856.25

If the quotient is a whole number, then 4 and 165,856.25 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:

1 663,425
-1 663,425
Keep dividing by the next highest number until you cannot divide anymore.

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

157172535851191752234255951,1151,5612,9753,7915,5757,80518,95526,53739,02594,775132,685663,425
-1-5-7-17-25-35-85-119-175-223-425-595-1,115-1,561-2,975-3,791-5,575-7,805-18,955-26,537-39,025-94,775-132,685-663,425

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