Q: What are the factor combinations of the number 150,455?

 A:
Positive:   1 x 1504555 x 30091
Negative: -1 x -150455-5 x -30091


How do I find the factor combinations of the number 150,455?

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 150,455, 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.

1 150,455
-1 -150,455

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 150,455.

Example:
1 x 150,455 = 150,455
and
-1 x -150,455 = 150,455
Notice both answers equal 150,455

With that explanation out of the way, let's continue. Next, we take the number 150,455 and divide it by 2:

150,455 ÷ 2 = 75,227.5

If the quotient is a whole number, then 2 and 75,227.5 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:

1 150,455
-1 -150,455

Now, we try dividing 150,455 by 3:

150,455 ÷ 3 = 50,151.6667

If the quotient is a whole number, then 3 and 50,151.6667 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:

1 150,455
-1 -150,455

Let's try dividing by 4:

150,455 ÷ 4 = 37,613.75

If the quotient is a whole number, then 4 and 37,613.75 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:

1 150,455
-1 150,455
Keep dividing by the next highest number until you cannot divide anymore.

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

1530,091150,455
-1-5-30,091-150,455

More Examples

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