It is currently 21 Mar 2018, 09:59

# Live Now:

GMAT Ninja Live : Word Translations | UVA Darden R2 Results - Join CHAT ROOM for Live Updates  | HBS R2 Results at Noon ET

### 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

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

Track

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44388
If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

09 Jul 2012, 03:31
Expert's post
10
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:35) correct 11% (00:44) wrong based on 1414 sessions

### HideShow timer Statistics

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

Diagnostic Test
Question: 18
Page: 22
Difficulty: 500
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 44388
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

09 Jul 2012, 03:32
Expert's post
2
This post was
BOOKMARKED
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.

_________________
Manager
Joined: 07 Sep 2011
Posts: 62
Location: United States
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

11 Jul 2012, 00:16
Difficulty Sub 550

8! has factors of 2, 3, 5 and 7 as 4 and 8 has 2 and six has 3. thus answer is A.
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 606
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

19 Jul 2012, 04:11
2
KUDOS
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!)

Hope it Helps!
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Manager
Joined: 26 Dec 2011
Posts: 111
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

25 Jul 2012, 05:46
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?
Senior Manager
Joined: 23 Oct 2010
Posts: 370
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

25 Aug 2012, 10:12
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

I am still on all gmat forums. msg me if you want to ask me smth

Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 512
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

10 Oct 2013, 17:08
2
This post was
BOOKMARKED
n = 8!

Prime factorization of 8!
= 1, 2, 3, 2*2, 5, 2*3, 7, 2*2*2

= 2, 3, 5, 7

= 4 prime factors > 1
Manager
Joined: 12 Jan 2013
Posts: 212
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

17 Dec 2013, 09:11
8! = 1x2x3x4x5x6x7x8.. Just do prime factorization of each integer alone and then count the number of different primes in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 878
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

04 May 2015, 06:42
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
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
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2503
GRE 1: 323 Q169 V154
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

03 Dec 2016, 19:48
Here is my solution =>
n=$$8! =>8*7*6*5*4*3*2*1=> 2^7*3^2*5*7$$=> Clearly it has 4 prime factors.
Hence A
(Additionally it has -> 8*3*2*2 =>96 factors )
_________________

Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3366
Location: India
GPA: 3.5
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

04 Dec 2016, 11:11
Bunuel 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

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

There can be only 4 different prime factors greater than 1 , as highlighted in Blue above..

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Joined: 30 Mar 2016
Posts: 47
If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

11 May 2017, 09:20
Hi e-GMAT

This Takeway: Number of prime factors of n! will be simply the number of prime numbers less than n: is true if n = even

For example:

n = 4 => n! = 1 x 2 x 3 x 4 So, different prime factors of 4! are: 2 & 3 which are less than n = 4

BUT once n = odd, Number of prime factors of n! will be simply the number of prime numbers less than OR EQUAL to n.

For example:

n = 7 => n! = 7! = 1 x 2 x 3 x 4 x 5 x 6 x 7 So different prime factors of 7! = 2, 3, 5, & 7. In this scenario, the prime number 7 is equal to n = 7.

So, the Takeaway would be: Number of prime factors of n! will be simply the number of prime numbers less than OR EQUAL to n.

Is this revised Takeaway correct?

Many thanks
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2127
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

16 May 2017, 18:12
Bunuel 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 = 8 x 7 x 6 x 5 x 4 x 3 x 2

We can prime factorize and we have:

n = 2^7 x 3^2 x 5^1 x 7^1

Thus, n has 4 different prime factors.

Alternate solution:

In general, the number of distinct prime factors that k! (where k > 1) has is the number of prime numbers less than or equal to k. We have n = 8!, so k = 8; the number of prime numbers less than or equal to 8 is 4, namely, 2, 3, 5 and 7.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Status: Don't watch the clock,Do what it does, Keep Going.
Joined: 10 Jan 2017
Posts: 46
Re: If n is the product of the integers from 1 to 8, inclusive [#permalink]

### Show Tags

23 Sep 2017, 08:34
Prime factors are those numbers which are only divisible by one and itself.prime factors between 1 to 8 inclusive are 2,3,5,7. So, answer is 4.
Re: If n is the product of the integers from 1 to 8, inclusive   [#permalink] 23 Sep 2017, 08:34
Display posts from previous: Sort by