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What is the smallest positive integer that has exactly 18 positive fac
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14 Apr 2020, 04:35
14 Apr 2020, 04:35
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Question Stats:
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What is the smallest positive integer that has exactly 18 positive factors?
A. 180
B. 216
C. 240
D. 256
E. None of the above
Are You Up For the Challenge: 700 Level Questions
A. 180
B. 216
C. 240
D. 256
E. None of the above
Are You Up For the Challenge: 700 Level Questions
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Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6065
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Location: India
GMAT: QUANT+DI EXPERT
GMAT 1: 750 Q51 V41
WE:Education (Education)
What is the smallest positive integer that has exactly 18 positive fac
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14 Apr 2020, 04:56
14 Apr 2020, 04:56
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Bunuel
What is the smallest positive integer that has exactly 18 positive factors?
A. 180
B. 216
C. 240
D. 256
E. None of the above
Are You Up For the Challenge: 700 Level Questions
A. 180
B. 216
C. 240
D. 256
E. None of the above
Are You Up For the Challenge: 700 Level Questions
If \(N = a^p*b^q*c^r...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)
STRATEGY:
-For smallest number the Prime number i.e. a, b, c etc must be as small as possible and
- Exponents of Primes should be broken into parts which makes the number smallest
- Bigger prime number must have smaller power to keep number as small as possible
-For smallest number the Prime number i.e. a, b, c etc must be as small as possible and
- Exponents of Primes should be broken into parts which makes the number smallest
- Bigger prime number must have smaller power to keep number as small as possible
18 = 9*2 = (8+1)*(1+1)
i.e. Number may be \(2^8*3^1 = 768\)
OR
18 = 6*3 = (5+1)*(2+1)
i.e. Number may be \(2^5*3^2 = 288\)
OR
18 = 2*3*3 = (1+1)*(2+1)*(2+1)
i.e. Number may be \(2^2*3^2*5 = 180\)
i.e. smallest such number must be 180
Answer: Option A
General Discussion
Re: What is the smallest positive integer that has exactly 18 positive fac
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14 Apr 2020, 12:48
14 Apr 2020, 12:48
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1
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Bunuel
What is the smallest positive integer that has exactly 18 positive factors?
A. 180
B. 216
C. 240
D. 256
E. None of the above
Are You Up For the Challenge: 700 Level Questions
A. 180
B. 216
C. 240
D. 256
E. None of the above
Are You Up For the Challenge: 700 Level Questions
I would suggest you go with the option.
1) 180= 2^2 * 3^2 * 5
formula to find total number o factors:
If x^a *y^b, total number of factors are (a+1)*(b+1)
In the ques, total number of factors are (2+1)(2+1)(1+1) = 18.
No need to check other options. Though if you want you may.
Answer is A.
Feel free to add kudos if you like the explanation.
