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If n is the product of the integers from 1 to 8...

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If n is the product of the integers from 1 to 8...

by swerve » Tue Dec 19, 2017 10:39 am
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.
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by EconomistGMATTutor » Tue Dec 19, 2017 10:49 am
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.
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by Brent@GMATPrepNow » Fri Jan 10, 2020 5:29 am
swerve wrote: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
n = (1)(2)(3)(4)(5)(6)(7)(8)
= (1)(2)(3)(2)(2)(5)(2)(3)(7)(2)(2)(2)
The prime factors are 2, 3, 5 and 7

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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