Q: What are the factor combinations of the number 504,175?

 A:
Positive:   1 x 5041755 x 1008357 x 7202525 x 2016735 x 1440543 x 1172567 x 7525175 x 2881215 x 2345301 x 1675335 x 1505469 x 1075
Negative: -1 x -504175-5 x -100835-7 x -72025-25 x -20167-35 x -14405-43 x -11725-67 x -7525-175 x -2881-215 x -2345-301 x -1675-335 x -1505-469 x -1075


How do I find the factor combinations of the number 504,175?

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 504,175, 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.

1 504,175
-1 -504,175

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 504,175.

Example:
1 x 504,175 = 504,175
and
-1 x -504,175 = 504,175
Notice both answers equal 504,175

With that explanation out of the way, let's continue. Next, we take the number 504,175 and divide it by 2:

504,175 ÷ 2 = 252,087.5

If the quotient is a whole number, then 2 and 252,087.5 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:

1 504,175
-1 -504,175

Now, we try dividing 504,175 by 3:

504,175 ÷ 3 = 168,058.3333

If the quotient is a whole number, then 3 and 168,058.3333 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:

1 504,175
-1 -504,175

Let's try dividing by 4:

504,175 ÷ 4 = 126,043.75

If the quotient is a whole number, then 4 and 126,043.75 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:

1 504,175
-1 504,175
Keep dividing by the next highest number until you cannot divide anymore.

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

157253543671752153013354691,0751,5051,6752,3452,8817,52511,72514,40520,16772,025100,835504,175
-1-5-7-25-35-43-67-175-215-301-335-469-1,075-1,505-1,675-2,345-2,881-7,525-11,725-14,405-20,167-72,025-100,835-504,175

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