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If m, p, and t are distinct positive prime numbers, then (m^
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14 Aug 2020, 10:49
14 Aug 2020, 10:49
Expert Reply
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Question Stats:
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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
a. 8
b. 9
c. 12
d. 15
e. 27
Re: If m, p, and t are distinct positive prime numbers, then (m^
[#permalink]
14 Aug 2020, 10:49
14 Aug 2020, 10:49
Expert Reply
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Re: If m, p, and t are distinct positive prime numbers, then (m^
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14 Aug 2020, 10:52
14 Aug 2020, 10:52
3
Carcass 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
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
