Q: What are the factor combinations of the number 150,434,249?

 A:
Positive:   1 x 1504342497 x 2149060779 x 1904231199 x 755951553 x 2720331367 x 1100471393 x 1079939569 x 15721
Negative: -1 x -150434249-7 x -21490607-79 x -1904231-199 x -755951-553 x -272033-1367 x -110047-1393 x -107993-9569 x -15721


How do I find the factor combinations of the number 150,434,249?

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 150,434,249, 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.

1 150,434,249
-1 -150,434,249

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 150,434,249.

Example:
1 x 150,434,249 = 150,434,249
and
-1 x -150,434,249 = 150,434,249
Notice both answers equal 150,434,249

With that explanation out of the way, let's continue. Next, we take the number 150,434,249 and divide it by 2:

150,434,249 ÷ 2 = 75,217,124.5

If the quotient is a whole number, then 2 and 75,217,124.5 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:

1 150,434,249
-1 -150,434,249

Now, we try dividing 150,434,249 by 3:

150,434,249 ÷ 3 = 50,144,749.6667

If the quotient is a whole number, then 3 and 50,144,749.6667 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:

1 150,434,249
-1 -150,434,249

Let's try dividing by 4:

150,434,249 ÷ 4 = 37,608,562.25

If the quotient is a whole number, then 4 and 37,608,562.25 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:

1 150,434,249
-1 150,434,249
Keep dividing by the next highest number until you cannot divide anymore.

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

17791995531,3671,3939,56915,721107,993110,047272,033755,9511,904,23121,490,607150,434,249
-1-7-79-199-553-1,367-1,393-9,569-15,721-107,993-110,047-272,033-755,951-1,904,231-21,490,607-150,434,249

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