Q: What are the factor combinations of the number 725,203?

 A:
Positive:   1 x 72520317 x 4265929 x 25007493 x 1471
Negative: -1 x -725203-17 x -42659-29 x -25007-493 x -1471


How do I find the factor combinations of the number 725,203?

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 725,203, 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.

1 725,203
-1 -725,203

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 725,203.

Example:
1 x 725,203 = 725,203
and
-1 x -725,203 = 725,203
Notice both answers equal 725,203

With that explanation out of the way, let's continue. Next, we take the number 725,203 and divide it by 2:

725,203 ÷ 2 = 362,601.5

If the quotient is a whole number, then 2 and 362,601.5 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:

1 725,203
-1 -725,203

Now, we try dividing 725,203 by 3:

725,203 ÷ 3 = 241,734.3333

If the quotient is a whole number, then 3 and 241,734.3333 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:

1 725,203
-1 -725,203

Let's try dividing by 4:

725,203 ÷ 4 = 181,300.75

If the quotient is a whole number, then 4 and 181,300.75 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:

1 725,203
-1 725,203
Keep dividing by the next highest number until you cannot divide anymore.

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

117294931,47125,00742,659725,203
-1-17-29-493-1,471-25,007-42,659-725,203

More Examples

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