Q: What are the factor combinations of the number 520,025?

 A:
Positive:   1 x 5200255 x 10400511 x 4727525 x 2080131 x 1677555 x 945561 x 8525155 x 3355275 x 1891305 x 1705341 x 1525671 x 775
Negative: -1 x -520025-5 x -104005-11 x -47275-25 x -20801-31 x -16775-55 x -9455-61 x -8525-155 x -3355-275 x -1891-305 x -1705-341 x -1525-671 x -775


How do I find the factor combinations of the number 520,025?

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 520,025, 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.

1 520,025
-1 -520,025

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 520,025.

Example:
1 x 520,025 = 520,025
and
-1 x -520,025 = 520,025
Notice both answers equal 520,025

With that explanation out of the way, let's continue. Next, we take the number 520,025 and divide it by 2:

520,025 ÷ 2 = 260,012.5

If the quotient is a whole number, then 2 and 260,012.5 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:

1 520,025
-1 -520,025

Now, we try dividing 520,025 by 3:

520,025 ÷ 3 = 173,341.6667

If the quotient is a whole number, then 3 and 173,341.6667 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:

1 520,025
-1 -520,025

Let's try dividing by 4:

520,025 ÷ 4 = 130,006.25

If the quotient is a whole number, then 4 and 130,006.25 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:

1 520,025
-1 520,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1511253155611552753053416717751,5251,7051,8913,3558,5259,45516,77520,80147,275104,005520,025
-1-5-11-25-31-55-61-155-275-305-341-671-775-1,525-1,705-1,891-3,355-8,525-9,455-16,775-20,801-47,275-104,005-520,025

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