Let P(M) Is 2^m Where M Is the Number of Distinct Prime Numbers in the Prime Factorization of M
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If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 
21 Apr 2016, 21:52
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If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 21 Apr 2016, 22:18
happyface101 wrote:
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
Number of factors of (2^a)*(3^b)*(5^c) ... = (a+1)(b+1)(c+1) ...
If m, p and t are the distinct prime numbers, then the number is already represented in its prime factorization form
Number of factors = (3+1)(1+1)(1+1) = 16
Out of these, one factor would be 1.
Hence different positive factors greater than 1 = 15
Correct Option: D
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If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] Updated on: 20 Sep 2020, 02:39
happyface101 wrote:
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
Method 1:
Let Number is \((m^3)(p)(t) = (2^3)(3)(5) = 120\)
We can write 120 as product of two numbers in following ways
1*120
2*60
3*40
4*30
5*24
6*20
8*15
10*12
8 cases = 8*2 i.e. 16 factors (including 1)
Factors greater than 1 = 15
Method 2:
CONCEPT: If \(N = a^p*b^q*c^r...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)
So factors of \((m^3)(p)(t)\) will be \((3+1)(1+1)(1+1) = 16\) but these factors include 1 as well
therefore factors of \((m^3)(p)(t)\) greater than 1 = 16-1 = 15
Answer: Option D
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Originally posted by GMATinsight on 22 Apr 2016, 03:42.
Last edited by GMATinsight on 20 Sep 2020, 02:39, edited 1 time in total.
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 02 May 2016, 20:04
Okay what does "positive " prime numbers signify here ?
Can primes be negative too ?
NEVER EVER EVER.
Regards
StoneCold
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 03 May 2016, 09:08
I wonder that 16 is not among the answers))
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 03 May 2016, 23:37
Konstantin1983 wrote:
I wonder that 16 is not among the answers))
You need factors greater than 1. So the number of factors is 16 - 1 = 15.
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 08 May 2016, 13:24
VeritasPrepKarishma wrote:
Konstantin1983 wrote:
I wonder that 16 is not among the answers))
You need factors greater than 1. So the number of factors is 16 - 1 = 15.
Yes i understand this. But GMAT likes to use traps so one can forget to exclude 1 and choose 16. But this answer is not present
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 14 Mar 2017, 16:27
I don't get this one. Is it a formula that you add +1 to each exponent to get # of factors?
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 14 Mar 2017, 19:50
kimbercs wrote:
I don't get this one. Is it a formula that you add +1 to each exponent to get # of factors?
Yes, the formula has been discussed here:
https://www.veritasprep.com/blog/2010/1 ... ly-number/
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 20 Mar 2017, 05:48
happyface101 wrote:
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
To determine the total number of factors of a number, we can add 1 to the exponent of each distinct prime number and multiply together the resulting numbers.
Thus, (m^3)(p)(t) = (m^3)(p^1)(t^1) has (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16 total factors. Since 1 is one of those 16 factors, there are actually 15 different positive factors greater than 1.
Answer: D
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 21 Mar 2017, 03:22
happyface101 wrote:
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
total number of factors = (3+1)(1+1)(1+1) = 16
except 1 number of factors = 16-1 = 15
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 02 Apr 2017, 23:02
m^3*p*t
Total no. of factors= (3+1)(1+1)(1+1)= 4*2*2=16
But 1 is excluded. Therefore the answer is 16-1=15
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 01 Mar 2018, 09:34
happyface101 wrote:
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
----ASIDE---------------------
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
-----ONTO THE QUESTION!!----------------------------
(m^3)(p)(t) = (m^3)(p^1)(t^1)
So, the number of positive divisors of (m^3)(p)(t) = (3+1)(1+1)(1+1) = (4)(2)(2) = 16
IMPORTANT: We have included 1 as one of the 16 factors in our solution above, but the question asks us to find the number of positive factors greater than 1.
So, the answer to the question = 16 - 1 = 15
Answer: D
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 27 Aug 2020, 10:09
stonecold wrote:
Okay what does "positive " prime numbers signify here ?
Can primes be negative too ?
NEVER EVER EVER.
Regards
StoneCold
Are you sure about that?
I read contrasting opinions on Google.
Could please an expert help us?
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 27 Aug 2020, 10:29
Genoa2000 wrote:
stonecold wrote:
Okay what does "positive " prime numbers signify here ?
Can primes be negative too ?
NEVER EVER EVER.
Regards
StoneCold
Are you sure about that?
I read contrasting opinions on Google.
Could please an expert help us?
From the GMAT Official Guide:
A prime number is a positive integer that has exactly two different positive divisors, 1 and itself.
For example, 2, 3, 5, 7, 11, and 13 are prime numbers, but 15 is not, since 15 has four different positive divisors, 1, 3, 5, and 15.
The number 1 is not a prime number since it has only one positive divisor.
Every integer greater than 1 either is prime or can be uniquely expressed as a product of prime factors. For example, 14 = (2)(7), 81 = (3)(3)(3)(3), and 484 = (2)(2)(11)(11).
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 27 Aug 2020, 10:37
Asked: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
Total number of positive factors of (m^3)(p)(t) = 4*2*2 = 16
Number of different positive factors greater than 1 = 16- 1 = 15
IMO D
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 27 Aug 2020, 11:54
BrentGMATPrepNow wrote:
Genoa2000 wrote:
stonecold wrote:
Okay what does "positive " prime numbers signify here ?
Can primes be negative too ?
NEVER EVER EVER.
Regards
StoneCold
Are you sure about that?
I read contrasting opinions on Google.
Could please an expert help us?
From the GMAT Official Guide:
A prime number is a positive integer that has exactly two different positive divisors, 1 and itself.
For example, 2, 3, 5, 7, 11, and 13 are prime numbers, but 15 is not, since 15 has four different positive divisors, 1, 3, 5, and 15.
The number 1 is not a prime number since it has only one positive divisor.
Every integer greater than 1 either is prime or can be uniquely expressed as a product of prime factors. For example, 14 = (2)(7), 81 = (3)(3)(3)(3), and 484 = (2)(2)(11)(11).
Thank you very much, Brent, you are always kind!
Bunuel you should add this fact to "All you need for quant"
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink] 15 Sep 2021, 03:10
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Re: If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) [#permalink]
15 Sep 2021, 03:10
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Let P(M) Is 2^m Where M Is the Number of Distinct Prime Numbers in the Prime Factorization of M
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