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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If m, p, and t are distinct positive prime numbers tagged by: M7MBA ##### This topic has 3 expert replies and 0 member replies ## If m, p, and t are distinct positive prime numbers 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 The OA is the option D. How can I know the number of factor without knowing the value of m, p and t? Experts, may you give me some help here? Please. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12422 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 Top Reply M7MBA 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 Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1776 messages Followed by: 14 members Upvotes: 43 M7MBA 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 factor 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 _________________ Scott Woodbury-Stewart Founder and CEO Joined 31 Dec 1969 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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