Q: What are the factor combinations of the number 90,840,209?

 A:
Positive:   1 x 9084020929 x 313242143 x 211256397 x 936497751 x 1209591247 x 728472813 x 322934171 x 21779
Negative: -1 x -90840209-29 x -3132421-43 x -2112563-97 x -936497-751 x -120959-1247 x -72847-2813 x -32293-4171 x -21779


How do I find the factor combinations of the number 90,840,209?

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 90,840,209, 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 90,840,209
-1 -90,840,209

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 90,840,209.

Example:
1 x 90,840,209 = 90,840,209
and
-1 x -90,840,209 = 90,840,209
Notice both answers equal 90,840,209

With that explanation out of the way, let's continue. Next, we take the number 90,840,209 and divide it by 2:

90,840,209 ÷ 2 = 45,420,104.5

If the quotient is a whole number, then 2 and 45,420,104.5 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 90,840,209
-1 -90,840,209

Now, we try dividing 90,840,209 by 3:

90,840,209 ÷ 3 = 30,280,069.6667

If the quotient is a whole number, then 3 and 30,280,069.6667 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 90,840,209
-1 -90,840,209

Let's try dividing by 4:

90,840,209 ÷ 4 = 22,710,052.25

If the quotient is a whole number, then 4 and 22,710,052.25 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 90,840,209
-1 90,840,209
Keep dividing by the next highest number until you cannot divide anymore.

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

12943977511,2472,8134,17121,77932,29372,847120,959936,4972,112,5633,132,42190,840,209
-1-29-43-97-751-1,247-2,813-4,171-21,779-32,293-72,847-120,959-936,497-2,112,563-3,132,421-90,840,209

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