Q: What are the factor combinations of the number 516,925?

 A:
Positive:   1 x 5169255 x 10338523 x 2247525 x 2067729 x 1782531 x 16675115 x 4495145 x 3565155 x 3335575 x 899667 x 775713 x 725
Negative: -1 x -516925-5 x -103385-23 x -22475-25 x -20677-29 x -17825-31 x -16675-115 x -4495-145 x -3565-155 x -3335-575 x -899-667 x -775-713 x -725


How do I find the factor combinations of the number 516,925?

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 516,925, 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.

1 516,925
-1 -516,925

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 516,925.

Example:
1 x 516,925 = 516,925
and
-1 x -516,925 = 516,925
Notice both answers equal 516,925

With that explanation out of the way, let's continue. Next, we take the number 516,925 and divide it by 2:

516,925 ÷ 2 = 258,462.5

If the quotient is a whole number, then 2 and 258,462.5 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:

1 516,925
-1 -516,925

Now, we try dividing 516,925 by 3:

516,925 ÷ 3 = 172,308.3333

If the quotient is a whole number, then 3 and 172,308.3333 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:

1 516,925
-1 -516,925

Let's try dividing by 4:

516,925 ÷ 4 = 129,231.25

If the quotient is a whole number, then 4 and 129,231.25 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:

1 516,925
-1 516,925
Keep dividing by the next highest number until you cannot divide anymore.

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

15232529311151451555756677137257758993,3353,5654,49516,67517,82520,67722,475103,385516,925
-1-5-23-25-29-31-115-145-155-575-667-713-725-775-899-3,335-3,565-4,495-16,675-17,825-20,677-22,475-103,385-516,925

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