GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jun 2019, 00:18 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  How many factors greater than 1 do 120, 210, and 270 have in common?

Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55682
How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags 00:00

Difficulty:   75% (hard)

Question Stats: 46% (01:52) correct 54% (01:39) wrong based on 109 sessions

HideShow timer Statistics

How many factors greater than 1 do 120, 210, and 270 have in common?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Thirty

_________________
CEO  P
Joined: 18 Aug 2017
Posts: 3889
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

+ IMO option B 3:
How many factors greater than 1 do 120, 210, and 270 have in common?
120: 2^2*3^1*5^1
210: 2^1*3*1^5^2
270:2^1*3^3*5^1

2,3,5 are common factors greater than 1
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern  B
Joined: 05 Jun 2018
Posts: 24
Location: United States (TN)
GMAT 1: 730 Q47 V44 GPA: 3
How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

2
We are looking for all shared factors of 120, 210, and 270 that are greater than 1.

The greatest common factor of 120, 210, and 270 is 30.

30 = (2)(3)(5)

We need to find all of the factors of the greatest common factor. To do so, we add 1 to each exponent of the prime factors of 30 and then multiply those numbers.

Each prime factor of 30 is only raised to the first power, thus, after increasing each of their powers by 1, the product of their exponents will be:

(2)(2)(2) = 8

There are 8 tots factors of 30. This includes the number 1. We were asked to find all common factors greater than 1. So, we will subtract 1 from 8.

Total number of factors shared among 120, 210, and 270

8 - 1 = 7

To summarize: to find all of the factors shared among 120, 210 and 270, we needed to determine the greatest common factor. Once we determined the GCF to be 30, we needed to find the total number of factors of 30. Lastly, we need to remember that the question asked about the number of factors that are greater than 1.

Posted from my mobile device
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
WE: Supply Chain Management (Energy and Utilities)
How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

Bunuel wrote:
How many factors greater than 1 do 120, 210, and 270 have in common?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Thirty

We have GCD(120,210,270)=30

Writing 30 in it's prime factorization form :- $$30=2^1*3^1*5^1$$
No of different factors of 30:- (1+1)*(1+1)*(1+1)=8
These 8 factors is including 1, but we are told to determine the factors greater than 1.

So the required number of factors: 7

Ans. (D)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 13 Aug 2018, 22:01.
Last edited by PKN on 13 Aug 2018, 23:25, edited 1 time in total.
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3373
Location: India
GPA: 3.12
How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

archish3113 wrote:
+ IMO option B 3:
How many factors greater than 1 do 120, 210, and 270 have in common?
120: 2^2*3^1*5^1
210: 2^1*3*1^5^2
270:2^1*3^3*5^1

2,3,5 are common factors greater than 1

Hey archish3113

Agreed that 2,3, and 5 are the only common prime factors greater than 1.

However, 6(2*3),10(2*5),15(3*5),30(2*3*5) are also common factors which you seem to have forgotten.

Therefore, the total number of common factors are 7(2,3,5,6,10,15, and 30)

Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got
Intern  B
Joined: 04 May 2014
Posts: 45
Concentration: Strategy, Operations
Re: How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

PKN wrote:
Bunuel wrote:
How many factors greater than 1 do 120, 210, and 270 have in common?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Thirty

We have LCM(120,210,270)=30

Writing 30 in it's prime factorization form :- $$30=2^1*3^1*5^1$$
No of different factors of 30:- (1+1)*(1+1)*(1+1)=8
These 8 factors is including 1, but we are told to determine the factors greater than 1.

So the required number of factors: 7

Ans. (D)

I think you wanted to tell HCF / GCD of 120, 210, 270 is 30. Rather than LCM.

Also, can you please clarify how did you think of taking HCF and then finding its total number of factors rather than prime factorising all numbers and finding the common factors.

Sent from my SM-G610F using GMAT Club Forum mobile app
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
WE: Supply Chain Management (Energy and Utilities)
Re: How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

tatz wrote:
PKN wrote:
Bunuel wrote:
How many factors greater than 1 do 120, 210, and 270 have in common?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Thirty

We have LCM(120,210,270)=30

Writing 30 in it's prime factorization form :- $$30=2^1*3^1*5^1$$
No of different factors of 30:- (1+1)*(1+1)*(1+1)=8
These 8 factors is including 1, but we are told to determine the factors greater than 1.

So the required number of factors: 7

Ans. (D)

I think you wanted to tell HCF / GCD of 120, 210, 270 is 30. Rather than LCM.

Also, can you please clarify how did you think of taking HCF and then finding its total number of factors rather than prime factorising all numbers and finding the common factors.

Sent from my SM-G610F using GMAT Club Forum mobile app

Quote:
I think you wanted to tell HCF / GCD of 120, 210, 270 is 30. Rather than LCM.

You are correct, calculated GCD.(NOT LCM)

Quote:
Also, can you please clarify how did you think of taking HCF and then finding its total number of factors rather than prime factorising all numbers and finding the common factors.

Thought process:-
1. We are told to determine the maximum no of common factors of three numbers. (All factors must be greater than 1)
2. If a number is divisible by its highest factor, then that number is also divisible by all of the factors of the highest factor. (
3. What is the magnitude of highest factor of 'n' nos of numbers? GCD is the answer. Then calculate GCD. This is the highest number which divides all the numbers under discussion.
4.Now apply 2 above. Calculate the no of factors of the GCD. The no of factors of a number is calculated using prime factorization method as explained.
5. Since the no of factors is inclusive of 1, so the required no of factors will be 1 less the total no of factors.

Thanking you.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern  B
Joined: 14 Jan 2018
Posts: 45
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q50 V29 GPA: 3.8
WE: Engineering (Manufacturing)
Re: How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

We are looking for all common factors of 120, 210, and 270 that are greater than 1.

The greatest common factor of 120, 210, and 270 is 30.

30=2*3*5

Total of factors formed =2*2*2=8
(Inclusive of 1)

So total no of factors greater than 1 =8-1
7

Option D

Posted from my mobile device
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6567
Location: United States (CA)
Re: How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

Bunuel wrote:
How many factors greater than 1 do 120, 210, and 270 have in common?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Thirty

Breaking each integer into its prime factors, we have:

120 = 12 x 10 = 2^2 x 3 x 5

210 = 21 x 10 = 2 x 3 x 5 x 7

270 = 27 x 10 = 2 x 3^2 x 5

We see that the 3 numbers have the following prime factors in common: 2^1 x 3^1 x 5^1. Adding 1 to each exponent produces (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 factors, including the number 1. So we have 7 factors that are greater than 1.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP  G
Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: How many factors greater than 1 do 120, 210, and 270 have in common?  [#permalink]

Show Tags

Bunuel wrote:
How many factors greater than 1 do 120, 210, and 270 have in common?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Thirty

120 = 2*2*2*3*5
210 = 2* 3*5*7
270 = 3*3*3*2*5

Now we can just take out the common factors from above
2,3,5,6,10,15,30

Seven

D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: How many factors greater than 1 do 120, 210, and 270 have in common?   [#permalink] 01 Feb 2019, 10:02
Display posts from previous: Sort by

How many factors greater than 1 do 120, 210, and 270 have in common?  