Q: What are the factor combinations of the number 516,425?

 A:
Positive:   1 x 5164255 x 1032857 x 7377513 x 3972525 x 2065735 x 1475565 x 794591 x 5675175 x 2951227 x 2275325 x 1589455 x 1135
Negative: -1 x -516425-5 x -103285-7 x -73775-13 x -39725-25 x -20657-35 x -14755-65 x -7945-91 x -5675-175 x -2951-227 x -2275-325 x -1589-455 x -1135


How do I find the factor combinations of the number 516,425?

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 516,425, 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.

1 516,425
-1 -516,425

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 516,425.

Example:
1 x 516,425 = 516,425
and
-1 x -516,425 = 516,425
Notice both answers equal 516,425

With that explanation out of the way, let's continue. Next, we take the number 516,425 and divide it by 2:

516,425 ÷ 2 = 258,212.5

If the quotient is a whole number, then 2 and 258,212.5 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:

1 516,425
-1 -516,425

Now, we try dividing 516,425 by 3:

516,425 ÷ 3 = 172,141.6667

If the quotient is a whole number, then 3 and 172,141.6667 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:

1 516,425
-1 -516,425

Let's try dividing by 4:

516,425 ÷ 4 = 129,106.25

If the quotient is a whole number, then 4 and 129,106.25 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:

1 516,425
-1 516,425
Keep dividing by the next highest number until you cannot divide anymore.

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

15713253565911752273254551,1351,5892,2752,9515,6757,94514,75520,65739,72573,775103,285516,425
-1-5-7-13-25-35-65-91-175-227-325-455-1,135-1,589-2,275-2,951-5,675-7,945-14,755-20,657-39,725-73,775-103,285-516,425

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