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.

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]
22 Feb 2011, 17:01

3

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

52% (02:45) correct
48% (01:39) wrong based on 190 sessions

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?

Re: The greatest common factor of 16 and the positive integer n [#permalink]
22 Feb 2011, 18:38

6

This post received KUDOS

Expert's post

ajit257 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?

3

14

30

42

70

i am not so sure about the oa.

GCF (n, 16) = 4 This means 4 is a factor of n but 8 and 16 are not. (If 8 were a factor of n too, the GCF would have been 8. Similarly for 16)

GCF (n, 45) = 3 This means 3 is a factor of n but 9 and 5 are not. Same logic as above.

210 = 2*3*5*7 n has 4 and 3 as factors and it doesn't have 5 as a factor. so GCF of n and 210 could be 6 (if 7 is not a factor of n) or 42 (if 7 is a factor of n)

Answer (D)

Note: 3 is definitely not the GCF of n and 210 because they definitely have 3*2 in common. So GCF has to be at least 6. _________________

Re: The greatest common factor of 16 and the positive integer n [#permalink]
22 Feb 2011, 18:59

1

This post received KUDOS

Expert's post

ajit257 wrote:

thanks Karishma ...my doubt is exactly the same thing but for 16 ..how come 42 is correct if n and 16 have a gcf of 4

That is because 210 has only one 2. Even though n has a 4 as factor, 210 does not. Therefore GCF of n and 210 does not have 4 as a factor. Does it make sense now? _________________

Re: The greatest common factor of 16 and the positive integer n [#permalink]
22 Feb 2011, 19:09

Expert's post

ajit257 wrote:

so lets say if another choice was given as 6 then what could have been the ans or it would not be that close.

Then there would have been two correct options: 6 and 42. Either can be the GCF of n and 210 depending on what exactly n is. GMAT never has 2 correct options and hence such a scenario is not possible. Only one of 6 and 42 would be in the answer choices. _________________

The greatest common factor of 16 and the positive integer n [#permalink]
25 Feb 2011, 07:21

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?

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).

Prime box of 16: 2, 2, 2, 2 Prime box of 45: 3, 3, 5

Prime box of 210: 2, 5, 3, 7

So, n has at least two 2's and one 3, but n hasn't got any 5. Now, checking alternatives: A) wrong, as n and 210 share at least one 2 and one 3. B) wrong again, no 3 in 14. C) wrong, as 30 has a 5 D) correct. 42 prime box is 2, 3, 7, so it meets all requirements. E) wrong, 70 prime box has 2, 7 and 5

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?

Re: Question on GCF [#permalink]
04 Nov 2012, 07:12

Some2609 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?

Haha, I just clicked wrong in the poll, but imho here goes the correct way:

16 and n - GCF = 4 = 2 x 2 45 and n - GCF = 3

210 = 2 x 3 x 5 x 7

Eliminate prime factors that are not included in the given options and approve the ones that appear. Eliminate: 5 Approve: 2, 3, 7

2 x 3 x 7 = 42 _________________

Exhaust your body, proceed your mind, cultivate your soul.

Re: Question on GCF [#permalink]
04 Nov 2012, 14:01

Expert's post

Some2609 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?

Merging similar topics. Refer to the solutions above and ask if anything remains unclear.

Re: The greatest common factor of 16 and the positive integer n [#permalink]
23 Jan 2014, 13:09

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 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).

Answer: D.

Hi Bunnel,

I have resolved this till n is a multiple of 2^2*3=12

why we are not considering 5 but we are considering 7.

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).

Answer: D.

Hi Bunnel,

I have resolved this till n is a multiple of 2^2*3=12

why we are not considering 5 but we are considering 7.

Thanks

Notice that the GCF of 45 (a multiple of 5) and n is 3 (not a multiple of 5). This means that n itself cannot be a multiple of 5.

As for 7: we know for sure that 2 and 3 are factors of n and 5 is not a factor of n. We know nothing about its other primes, so any prime greater than 5 theoretically can be a factor of n. _________________

Re: The greatest common factor of 16 and the positive integer n [#permalink]
03 Jun 2014, 05:56

1st pair (n and 16) for whom the GCF is 4

GCF=4=2^2 16=2^4 Since GCF contains the lowest powers of all the common prime factors it can be deducted that n must contain 2^2

2nd pair (n and 45)for whom the GCF is 3 GCF=3=3^1 45=3^(2 ) x 5^1 Since GCF contains the lowest powers of all the common prime factors it can be deducted that n must contain 3^1 and must not contain 5^1

3rd Pair (n and 210) 210=2 x 3x 5 x 7 n=must contain 2^2,must contain 3^1,may contain 7,must not contain 5 Therefore n could be either=(2^2 x 3^1=12)or (2^2 x 3^1 x 7^1=84)

if n=12 then GCF of 12 and 210 is 2 x 3=6 if n=84 then GCF of 84 and 210 is 2 x 3 x 7=42

The Cambridge open day wasn’t quite what I was used to; no sample lectures, no hard and heavy approach; and it even started with a sandwich lunch. Overall...

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...