Problem Solving

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Hi Swerve,
Let's take a look at your question.

n is the product of the integers from 1 to 8, inclusive.

$$n=1\times2\times3\times4\times5\times6\times7\times8$$ $$n=1\times2\times3\times\left(2\times2\right)\times5\times\left(2\times3\right)\times7\times\left(2\times2\times2\right)$$ $$n=1\times2\times2\times2\times2\times2\times2\times2\times3\times3\times5\times7$$

We can see that the product n has four different prime factors, 2, 3, 5, 7.

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.