Q: What are the factor combinations of the number 733,025?

 A:
Positive:   1 x 7330255 x 14660525 x 29321109 x 6725269 x 2725545 x 1345
Negative: -1 x -733025-5 x -146605-25 x -29321-109 x -6725-269 x -2725-545 x -1345


How do I find the factor combinations of the number 733,025?

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 733,025, 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.

1 733,025
-1 -733,025

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 733,025.

Example:
1 x 733,025 = 733,025
and
-1 x -733,025 = 733,025
Notice both answers equal 733,025

With that explanation out of the way, let's continue. Next, we take the number 733,025 and divide it by 2:

733,025 ÷ 2 = 366,512.5

If the quotient is a whole number, then 2 and 366,512.5 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:

1 733,025
-1 -733,025

Now, we try dividing 733,025 by 3:

733,025 ÷ 3 = 244,341.6667

If the quotient is a whole number, then 3 and 244,341.6667 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:

1 733,025
-1 -733,025

Let's try dividing by 4:

733,025 ÷ 4 = 183,256.25

If the quotient is a whole number, then 4 and 183,256.25 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:

1 733,025
-1 733,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15251092695451,3452,7256,72529,321146,605733,025
-1-5-25-109-269-545-1,345-2,725-6,725-29,321-146,605-733,025

More Examples

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