Events & Promotions
|
|
GMAT Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 1810:00 AM PDT
-11:00 AM PDT
Join us in a live GMAT practice session and solve 25 challenging GMAT questions with other test takers in timed conditions, covering GMAT Quant, Data Sufficiency, Data Insights, Reading Comprehension, and Critical Reasoning questions.
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products. Ends 6/1
May 1501:00 PM IST
-11:00 AM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.- May 19
12:00 PM PDT
-01:00 PM PDT
Scoring 329 on the GRE is not always about using more books, more courses, or a longer study plan. In this episode of GRE Success Talks, Ashutosh shares his GRE preparation strategy, study plan, and test-day experience, explaining how he kept his prep.... - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
09 Jul 2012, 03:31
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
92% (00:51) correct
8%
(01:10)
wrong
based on 4341
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) four
(B) five
(C) six
(D) seven
(E) eight
04 May 2015, 06:42
Kudos
Bookmarks
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.
x-is-the-largest-prime-number-less-than-positive-integer-n-p-is-an-in-197329.html
p-is-the-smallest-perfect-cube-greater-than-197336.html
Regards,
Krishna
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.
x-is-the-largest-prime-number-less-than-positive-integer-n-p-is-an-in-197329.html
p-is-the-smallest-perfect-cube-greater-than-197336.html
Regards,
Krishna
09 Jul 2012, 03:32
Kudos
Bookmarks
SOLUTION
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
\(n=8!\), so it has 4 prime factors: 2, 3, 5, and 7.
Answer: A.
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
\(n=8!\), so it has 4 prime factors: 2, 3, 5, and 7.
Answer: A.
