Q: What are the factor combinations of the number 150,270,523?

 A:
Positive:   1 x 15027052313 x 1155927123 x 6533501149 x 1008527299 x 5025771937 x 775793373 x 445513427 x 43849
Negative: -1 x -150270523-13 x -11559271-23 x -6533501-149 x -1008527-299 x -502577-1937 x -77579-3373 x -44551-3427 x -43849


How do I find the factor combinations of the number 150,270,523?

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 150,270,523, 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.

1 150,270,523
-1 -150,270,523

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 150,270,523.

Example:
1 x 150,270,523 = 150,270,523
and
-1 x -150,270,523 = 150,270,523
Notice both answers equal 150,270,523

With that explanation out of the way, let's continue. Next, we take the number 150,270,523 and divide it by 2:

150,270,523 ÷ 2 = 75,135,261.5

If the quotient is a whole number, then 2 and 75,135,261.5 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:

1 150,270,523
-1 -150,270,523

Now, we try dividing 150,270,523 by 3:

150,270,523 ÷ 3 = 50,090,174.3333

If the quotient is a whole number, then 3 and 50,090,174.3333 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:

1 150,270,523
-1 -150,270,523

Let's try dividing by 4:

150,270,523 ÷ 4 = 37,567,630.75

If the quotient is a whole number, then 4 and 37,567,630.75 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:

1 150,270,523
-1 150,270,523
Keep dividing by the next highest number until you cannot divide anymore.

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

113231492991,9373,3733,42743,84944,55177,579502,5771,008,5276,533,50111,559,271150,270,523
-1-13-23-149-299-1,937-3,373-3,427-43,849-44,551-77,579-502,577-1,008,527-6,533,501-11,559,271-150,270,523

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