Q: What are the factor combinations of the number 90,530,499?

 A:
Positive:   1 x 905304993 x 301768332797 x 323678391 x 10789
Negative: -1 x -90530499-3 x -30176833-2797 x -32367-8391 x -10789


How do I find the factor combinations of the number 90,530,499?

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 90,530,499, 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 90,530,499
-1 -90,530,499

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 90,530,499.

Example:
1 x 90,530,499 = 90,530,499
and
-1 x -90,530,499 = 90,530,499
Notice both answers equal 90,530,499

With that explanation out of the way, let's continue. Next, we take the number 90,530,499 and divide it by 2:

90,530,499 ÷ 2 = 45,265,249.5

If the quotient is a whole number, then 2 and 45,265,249.5 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 90,530,499
-1 -90,530,499

Now, we try dividing 90,530,499 by 3:

90,530,499 ÷ 3 = 30,176,833

If the quotient is a whole number, then 3 and 30,176,833 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 30,176,833 90,530,499
-1 -3 -30,176,833 -90,530,499

Let's try dividing by 4:

90,530,499 ÷ 4 = 22,632,624.75

If the quotient is a whole number, then 4 and 22,632,624.75 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 3 30,176,833 90,530,499
-1 -3 -30,176,833 90,530,499
Keep dividing by the next highest number until you cannot divide anymore.

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

132,7978,39110,78932,36730,176,83390,530,499
-1-3-2,797-8,391-10,789-32,367-30,176,833-90,530,499

More Examples

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