Q: What are the factor combinations of the number 259,835?

 A:
Positive:   1 x 2598355 x 51967157 x 1655331 x 785
Negative: -1 x -259835-5 x -51967-157 x -1655-331 x -785


How do I find the factor combinations of the number 259,835?

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 259,835, 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.

1 259,835
-1 -259,835

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 259,835.

Example:
1 x 259,835 = 259,835
and
-1 x -259,835 = 259,835
Notice both answers equal 259,835

With that explanation out of the way, let's continue. Next, we take the number 259,835 and divide it by 2:

259,835 ÷ 2 = 129,917.5

If the quotient is a whole number, then 2 and 129,917.5 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:

1 259,835
-1 -259,835

Now, we try dividing 259,835 by 3:

259,835 ÷ 3 = 86,611.6667

If the quotient is a whole number, then 3 and 86,611.6667 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:

1 259,835
-1 -259,835

Let's try dividing by 4:

259,835 ÷ 4 = 64,958.75

If the quotient is a whole number, then 4 and 64,958.75 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:

1 259,835
-1 259,835
Keep dividing by the next highest number until you cannot divide anymore.

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

151573317851,65551,967259,835
-1-5-157-331-785-1,655-51,967-259,835

More Examples

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