Q: What are the factor combinations of the number 109,089,259?

 A:
Positive:   1 x 109089259337 x 323707
Negative: -1 x -109089259-337 x -323707


How do I find the factor combinations of the number 109,089,259?

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 109,089,259, 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.

1 109,089,259
-1 -109,089,259

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 109,089,259.

Example:
1 x 109,089,259 = 109,089,259
and
-1 x -109,089,259 = 109,089,259
Notice both answers equal 109,089,259

With that explanation out of the way, let's continue. Next, we take the number 109,089,259 and divide it by 2:

109,089,259 ÷ 2 = 54,544,629.5

If the quotient is a whole number, then 2 and 54,544,629.5 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:

1 109,089,259
-1 -109,089,259

Now, we try dividing 109,089,259 by 3:

109,089,259 ÷ 3 = 36,363,086.3333

If the quotient is a whole number, then 3 and 36,363,086.3333 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:

1 109,089,259
-1 -109,089,259

Let's try dividing by 4:

109,089,259 ÷ 4 = 27,272,314.75

If the quotient is a whole number, then 4 and 27,272,314.75 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:

1 109,089,259
-1 109,089,259
Keep dividing by the next highest number until you cannot divide anymore.

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

1337323,707109,089,259
-1-337-323,707-109,089,259

More Examples

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