Q: What are the factor combinations of the number 597,025?

 A:
Positive:   1 x 5970255 x 11940511 x 5427513 x 4592525 x 2388155 x 1085565 x 9185143 x 4175167 x 3575275 x 2171325 x 1837715 x 835
Negative: -1 x -597025-5 x -119405-11 x -54275-13 x -45925-25 x -23881-55 x -10855-65 x -9185-143 x -4175-167 x -3575-275 x -2171-325 x -1837-715 x -835


How do I find the factor combinations of the number 597,025?

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 597,025, 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.

1 597,025
-1 -597,025

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 597,025.

Example:
1 x 597,025 = 597,025
and
-1 x -597,025 = 597,025
Notice both answers equal 597,025

With that explanation out of the way, let's continue. Next, we take the number 597,025 and divide it by 2:

597,025 ÷ 2 = 298,512.5

If the quotient is a whole number, then 2 and 298,512.5 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:

1 597,025
-1 -597,025

Now, we try dividing 597,025 by 3:

597,025 ÷ 3 = 199,008.3333

If the quotient is a whole number, then 3 and 199,008.3333 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:

1 597,025
-1 -597,025

Let's try dividing by 4:

597,025 ÷ 4 = 149,256.25

If the quotient is a whole number, then 4 and 149,256.25 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:

1 597,025
-1 597,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1511132555651431672753257158351,8372,1713,5754,1759,18510,85523,88145,92554,275119,405597,025
-1-5-11-13-25-55-65-143-167-275-325-715-835-1,837-2,171-3,575-4,175-9,185-10,855-23,881-45,925-54,275-119,405-597,025

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