Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]
19 Jul 2012, 03:11

n = 1*2*3*4*5*6*7*8

so only Prime numbers which will be factors of n will be 2,3,5,7 (as prime numbers which are greater than 7 will not be there in the product of 1 to 8!)

Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]
25 Jul 2012, 04:46

Is it correct to say prime factors greater than 1? 1 is not a prime factor at all. If one says prime factor greater than 2, then it does make sense. Am I right in making this statement?

Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]
25 Aug 2012, 09:12

yep, the phrase " different prime factors greater than 1" sounds strange, since in fact, all of these primes are different.furthermore, no need to point out about 1, since 1 is not prime. _________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]
10 Oct 2013, 09:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]
04 May 2015, 05:42

1

This post received KUDOS

Expert's post

In this question, I have noticed that many students are prime factorizing every term in the product to find out the answer. But is that necessary?

What if the expression was Z = 1*2*3*…*30. Would you have factorized every term?

Let's do a quick concept recap.

Concept Recap: Primes are the basic building blocks for every positive integer greater than 1. Every positive integer greater than 1 is itself a prime or a product of primes less than the number itself.

How is this related to the question?: Take the example of 6!. 6! as we all know is equal to \(1*2*3*4*5*6\). Obviously, we don't need to factorize every element in this expression to find out the different prime factors of 6!. Using the knowledge from the above concept recap that the different prime factors of 6! will be simply the prime numbers less than or equal to 6 itself, we can say the prime factors of 6! are 2, 3 and 5. Therefore 6! has 3 prime factors.

Answer for this question: Primes less than 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 (a total of 10 primes.). Therefore, if Z = 30!, then there would 10 different prime factors for Z.

In such questions, where you need to find the number of prime factors of a factorial expression, do not waste your time factorizing every term. Number of prime factors of n! will be simply the number of prime numbers less than n.

Footnote for the curious minded: It would have made sense to factorize every term in the expression, if the question had asked the "total number of factors" instead of "number of prime factors". To find the total number of factors, we definitely would need to find the prime factors and their powers in the expression.

You can take a stab at the following questions to test your understanding of these concepts.

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

A lot of readers have asked me what benefits the Duke MBA has brought me. The MBA is a huge upfront investment and the opportunity cost is high. Most...

I have not posted in more than a month! It has been a super busy period, wrapping things up at Universal Music, completing most of the admin tasks in preparation for Stanford...