Q: What are the factor combinations of the number 503,125?

 A:
Positive:   1 x 5031255 x 1006257 x 7187523 x 2187525 x 2012535 x 14375115 x 4375125 x 4025161 x 3125175 x 2875575 x 875625 x 805
Negative: -1 x -503125-5 x -100625-7 x -71875-23 x -21875-25 x -20125-35 x -14375-115 x -4375-125 x -4025-161 x -3125-175 x -2875-575 x -875-625 x -805


How do I find the factor combinations of the number 503,125?

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 503,125, 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.

1 503,125
-1 -503,125

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 503,125.

Example:
1 x 503,125 = 503,125
and
-1 x -503,125 = 503,125
Notice both answers equal 503,125

With that explanation out of the way, let's continue. Next, we take the number 503,125 and divide it by 2:

503,125 ÷ 2 = 251,562.5

If the quotient is a whole number, then 2 and 251,562.5 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:

1 503,125
-1 -503,125

Now, we try dividing 503,125 by 3:

503,125 ÷ 3 = 167,708.3333

If the quotient is a whole number, then 3 and 167,708.3333 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:

1 503,125
-1 -503,125

Let's try dividing by 4:

503,125 ÷ 4 = 125,781.25

If the quotient is a whole number, then 4 and 125,781.25 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:

1 503,125
-1 503,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1572325351151251611755756258058752,8753,1254,0254,37514,37520,12521,87571,875100,625503,125
-1-5-7-23-25-35-115-125-161-175-575-625-805-875-2,875-3,125-4,025-4,375-14,375-20,125-21,875-71,875-100,625-503,125

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