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

16 Sep 2008, 07:44

1

This post received KUDOS

12

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

53% (02:29) correct
47% (01:42) wrong based on 411 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?

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?

3 14 30 42 70

n= 4x, n= 3y ie: n= 12z ie: 3*2*2*z , z cant be 5 or 2 or 3

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?

3 14 30 42 70

since GCF of 16 and n is 4 16 = 2*2 * 2 * 2 n = 2*2 * ...

since GCF of 45 and n is 3 45 = 5 * 3 * 3 n = 3 * ...

thus n must be 2*2 *3 *...

210 = 7 * 3 * 5 * 2

n can not be 5, (otherwise GCF of 45 and 3 would have been 15) it can be 7 though

The greatest common factor of 16 and the positive integer n is 4 The prime factor of n will have exactly two 2s The greatest common factor of n and 45 is 3 Exactly one 3 and exactly zero 5s Because the question states that the GCD between n and 45 is only 3. Thus, 5 cannot be a factor of n, but 7 could be a factor.

Hence, 2*3*7=42.
_________________

Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general.

GCF of 16 and n = 4 => n = 2^2(...) -----1 GCF of n and 45 = 3 => n =3(...) -------2

GCF of n and 210 = ?

= GCF of (2^2)*3(...) and 2*3*5*7 = 6

so GCF of n and 210 would be multiple of 6.

Answer is D as its the only possible option that is a multiple of 6.

why should the GCF of n and 210 be multiple of 6?

Thank you all!!

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

20 Apr 2013, 12:29

1

This post received KUDOS

mun23 wrote:

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

Need easy explanation to solve it quickly

Hi, let me try to explain in simpler way:

GCF = 4 = 2^2 16 = 2^4 that means prime box of n = 2^2 , ? ? ?

GCF = 3 45 = 3^2*5 that means prime box of n = 3^1, ? ? ?

Overall prime box of n = 2^2, 3^1, ???

Now, 210 = 3*7*5*2 from above we know the prime factor and powers of n (not complete ??) therefore GCF = 3^1 * 2^1 * 7^1 (not 5 - we have seen above, but at least a 7 is possible) Thus at least a GCF of 42 is possible here

Hope this helps
_________________

"When the going gets tough, the tough gets going!"

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

Show Tags

20 Apr 2013, 21:48

1

This post received KUDOS

Simple explanation?

First, do a factor tree for each number.

You'll see that 5 can't be a factor of N (otherwise it would have been the highest factor between N and 45).

The highest factor that could theoretically exist between N and 210 is therefore all of the factors of 210 besides those we've ruled out. 210 is factored to 2 * 3 * 5 * 7. we've ruled out 5, so 2 * 3 * 7 = 42. Answer is D.

If the question asked "the highest factor that we KNOW exists" rather than "COULD" exist, the answer would be six since 2 and 3 are both factors of N, as well as of 210.

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

Show Tags

09 Jul 2014, 07:20

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.
_________________

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

Show Tags

01 Aug 2014, 23:49

n has to be a multiple of (2*2)*3 = 12 A common factor between 210= (2*3*5*7) and multiple of 12 is 2*3=6 So the G.C.F of n and 210 has to be a multiple of 6 The two choices that are multiples of 6 are 30 and 42. Bur n is not a multiple of 5 .So 30 can be ruled out and the answer is 42.
_________________

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

Show Tags

03 Oct 2015, 06:30

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

Show Tags

14 Mar 2016, 01:45

Here it is easy to come to the conclusion that 42 and 30 are both to be considered as the gcd must be a multiple of 6 but we need to discard 3 SO0 as 5 cannot be in N as if so the GCD of N and 45 will change hence 42 is correct So D
_________________

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

Show Tags

22 Mar 2017, 06:32

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.
_________________

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

Show Tags

22 Mar 2017, 08:51

dancinggeometry wrote:

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

n's factors of 3 and 4 make it a multiple of 12 with an odd multiplier not 9, 5, 3 or 1. 7*12=84=7*3*2*2=42*2 210=7*5*3*2=42*5 42 D

gmatclubot

The greatest common factor of 16 and the positive integer n
[#permalink]
22 Mar 2017, 08:51

Best Schools for Young MBA Applicants Deciding when to start applying to business school can be a challenge. Salary increases dramatically after an MBA, but schools tend to prefer...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...