What are the factors of 150 and 300?

Answer 1

Start with the prime factorization of 300:

300 = 2 X 150 = 2 X 3 X 50 = 2 X 3 X 5 X 10 = 2 X 3 X 5 X 2 X 5 = 22 X 3 X 52.

Using the result from above, we can see that the prime factorization of 150 is:

3 X 5 X 2 X 5 = 2 X 3 X 52.

To find every factor for these two numbers, we need to find every possible product, omitting repeated products, of all of the numbers of their respective prime factorizations.

Since 150 is a factor of 300, as shown above, we'll start there. That will give us the set of these two numbers' common factors.

2 X 3, 2 X 5, 2 X 3 X 5, 2 X 5 X 5, 3 X 5, 3 X 5 X 5, and 5 X 5 are all factors, as are 1, 150, and the prime factors 2, 3, and 5.

Thus, the set of all factors of 150 is:

{1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150}.

As stated before, these are all going to be factors of 300 as well, however 300 has some additional factors, namely:

2 X 2, 2 X 2 X 3, 2 X 2 X 5, 2 X 2 X 3 X 5, 2 X 2 X 5 X 5, and itself.

Thus, the set of all factors of 300 is:

{1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300}.