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 500,000 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:

The greatest common factor of 16 and the positive integer n [#permalink]

Show Tags

21 Dec 2008, 05:18

2

This post received KUDOS

12

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

54% (02:01) correct
46% (01:10) wrong based on 377 sessions

HideShow timer Statistics

The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

16 = 2^4. 16 and n have GCF as 2^2. That means, n could have only 2 twos as the factor.

45 = 5*3^2. 45 and have GCF as 3. That means, n will not have 5 as factor and only one 3 as the factor.

210 = 2*3*5*7 and since n does not have 5 as factor and n has 2^2 and 3 as factors, n could as well have 7 as a factor. Hence, 2*3*7 would be the greatest common factor.

The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? a) 3 b) 14 c) 30 d) 42 e) 70

The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? a) 3 b) 14 c) 30 d) 42 e) 70

210 = 5*2*3*7

N = 4x * 3 y = 2^2*3xy

6 must be the minimum common factor between n and 210. Answer must be divisible by 6

only 30 and 42 left. Maximum value could be 42.

If answer choice has 210 then will chose 210
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

i got up to the point where 6 = lowest common factor.

then i understand that the answer has to be divisible by 6, therefore 30 or 42. why not 30?

"Which of the following could be the greatest common factor of n and 210?" Question is asking about greatest common factor.. obviously.. 42>30.. so 42 is the answer.
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? a) 3 b) 14 c) 30 d) 42 e) 70

agree with 42.

16 = 2x2x2x2 45 = 3x3x5 n = 4 x 3 x k, where k is an integer 210 = 2x3x5x7

gcf of 16 and n = 4 gcf of n and 45 = 3 gcf of n and 210 = 2x3x7 (5 and 4 cannot be factors of n because 210 has only 2 as factor and n doesnot have 5 as factor) = 42

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.
_________________

The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

A. 3 B. 14 C. 30 D. 42 E. 70

The greatest common factor of 2^4=16 and n is 4 --> n is a multiple of 2^2=4 but not the higher powers of 2, for example 2^3=8 or 2^4=16, because if it were then the greatest common factor of 16 and n would be more than 4;

The greatest common factor of 3^2*5=45 and n is 3 --> n is a multiple of 3 but not the higher powers of 3 and not 5, because if it were then the greatest common factor of 3^2*5=45 and n would be more than 3;

So, n is a multiple of 2^2*3=12, not a multiple of higher powers of 2 or 3, and not a multiple of 5 (so n=12x where x could be any positive integer but 2, 3, or 5). Now, as 210=2*3*5*7 then the greatest common factor of n and 210 could be 6 or 6*7=42 (if 7 is a factor of n).

Re: The greatest common factor of 16 and the positive integer n [#permalink]

Show Tags

19 Apr 2014, 08:26

Not a proper but a random approach:

GCD(n,16) = 4

n--------------2^4

n must at least be a multiple of 4

GCD(n,45) = 3

n----------------------5*3^2

n must have one '3' and shouldn't have 5

Applying above restrictions calculating

Max GCD(n,210)

n-------------------------2*3*5*7

N has one 3 and one 4 so

n= 3*2*2

n cannot have 5 but can have 7 so

n=2*2*3*7 --------------------2*3*5*7

Max(GCD) = 42
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

gmatclubot

Re: The greatest common factor of 16 and the positive integer n
[#permalink]
19 Apr 2014, 08:26

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...