Q: What are the factor combinations of the number 502,075?

 A:
Positive:   1 x 5020755 x 1004157 x 7172519 x 2642525 x 2008335 x 1434595 x 5285133 x 3775151 x 3325175 x 2869475 x 1057665 x 755
Negative: -1 x -502075-5 x -100415-7 x -71725-19 x -26425-25 x -20083-35 x -14345-95 x -5285-133 x -3775-151 x -3325-175 x -2869-475 x -1057-665 x -755


How do I find the factor combinations of the number 502,075?

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 502,075, 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.

1 502,075
-1 -502,075

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 502,075.

Example:
1 x 502,075 = 502,075
and
-1 x -502,075 = 502,075
Notice both answers equal 502,075

With that explanation out of the way, let's continue. Next, we take the number 502,075 and divide it by 2:

502,075 ÷ 2 = 251,037.5

If the quotient is a whole number, then 2 and 251,037.5 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:

1 502,075
-1 -502,075

Now, we try dividing 502,075 by 3:

502,075 ÷ 3 = 167,358.3333

If the quotient is a whole number, then 3 and 167,358.3333 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:

1 502,075
-1 -502,075

Let's try dividing by 4:

502,075 ÷ 4 = 125,518.75

If the quotient is a whole number, then 4 and 125,518.75 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:

1 502,075
-1 502,075
Keep dividing by the next highest number until you cannot divide anymore.

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

157192535951331511754756657551,0572,8693,3253,7755,28514,34520,08326,42571,725100,415502,075
-1-5-7-19-25-35-95-133-151-175-475-665-755-1,057-2,869-3,325-3,775-5,285-14,345-20,083-26,425-71,725-100,415-502,075

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