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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 ## Gmat loves factors tagged by: Brent@GMATPrepNow ##### This topic has 5 expert replies and 2 member replies In the number 36 : 1>How many total factors ? 2>How many Odd factors ? 3>How many even factors ? 4>How many prime factors ? This is a self devised question, so no OA. BTW IMO answers are 1>9 2>3 3>6 4>2 Short cuts after expert opinions. _________________ Cheers !! Quant 47-Striving for 50 Verbal 34-Striving for 40 My gmat journey : https://www.beatthegmat.com/710-bblast-signing-off-thank-you-all-t90735.html My take on the GMAT RC : https://www.beatthegmat.com/ways-to-bblast-the-gmat-rc-t90808.html How to prepare before your MBA: https://www.youtube.com/watch?v=upz46D7l8fA&list=PLUmBNvYMnppJRMpR9fwfcsTWBZF14TKW_ ### GMAT/MBA Expert GMAT Instructor Joined 02 Apr 2010 Posted: 3835 messages Followed by: 523 members Upvotes: 1854 GMAT Score: 770 bblast wrote: In the number 36 : 1>How many total factors ? 2>How many Odd factors ? 3>How many even factors ? 4>How many prime factors ? 36 = (2^2)*(3^2) 1. Number of total factors = (Number of ways to select any number of 2's out of 2)*(Number of ways to select any number of 3's out of 2) = (2 + 1)*(2 + 1) = 9 2. Number of total odd factors = (Number of ways to select no 2)*(Number of ways to select any number of 3's out of 2) = 1*(2 + 1) = 3 3. Number of even factors = (Number of ways to select at least one 2 out of 2)*(Number of ways to select any number of 3's out of 2) = (2)*(2 + 1) = 6 4. Number of prime factors = 2 _________________ Anurag Mairal, Ph.D., MBA GMAT Expert, Admissions and Career Guidance Gurome, Inc. 1-800-566-4043 (USA) Join Our Facebook Groups GMAT with Gurome https://www.facebook.com/groups/272466352793633/ Admissions with Gurome https://www.facebook.com/groups/461459690536574/ Career Advising with Gurome https://www.facebook.com/groups/360435787349781/ Master | Next Rank: 500 Posts Joined 18 Jun 2010 Posted: 131 messages Upvotes: 10 Target GMAT Score: 700+ Anurag@Gurome, I'm not familiar with your method of breaking down total factors. Can you explain in a bit more detail? Thanks! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15386 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Quote: In the number 36 : 1>How many total factors ? 2>How many Odd factors ? 3>How many even factors ? 4>How many prime factors ? This is a self devised question, so no OA. BTW IMO answers are 1>9 2>3 3>6 4>2 To determine the number of positive factors of an integer: 1) Prime-factorize the integer 2) Add 1 to each exponent 3) Multiply 36 = 2^2 * 3^2. Adding 1 to each exponent and multiplying, we get (2+1)*(2+1) = 9 factors. Here's the reasoning. To determine how many factors can be created from 36 = 2^2 * 3^2, we need to determine the number of choices we have of each prime factor: For 2, we can use 2^0, 2^1, or 2^2, giving us 3 choices. For 3, we can use 3^0, 3^1, or 3^2, giving us 3 choices. Multiplying, we get 3*3 = 9 possible factors. Another example: How many positive factors does 882 have? 882 = 2 * 3^2 * 7^2. Adding 1 to each exponent and multiplying, we get 2*3*3 = 18 factors. To determine the number of odd positive factors of an integer: 1) Prime-factorize the integer 2) Add 1 to the exponent of each odd prime factor 3) Multiply 36 = 2^2 * 3^2. The only odd prime factor is 3, with an exponent of 2. Adding 1 to the exponent, we get 2+1 = 3 odd factors. Number of even positive factors = Total possible factors - Odd factors = 9-3 = 6. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Legendary Member Joined 03 Jun 2008 Posted: 502 messages Followed by: 21 members Upvotes: 99 So, to calculate EVEN POSITIVE FACTORS, we must find the total factors and subtract ODD POSITIVE FACTORS from it? From 36 = 2^2 * 3^2. Why can't we say that only EVEN prime factor is 2, with an exponent of 2 and adding 1 to the exponent, we get 2+1 = 3 EVEN factors ? _________________ - VK I will (Learn. Recognize. Apply) ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 aleph777 wrote: I'm not familiar with your method of breaking down total factors. Can you explain in a bit more detail? If N = (p^a)(q^b)(r^c)..., where p, q, r,...(etc.) are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)... Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = 5x4x2=40 Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15386 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 vk_vinayak wrote: So, to calculate EVEN POSITIVE FACTORS, we must find the total factors and subtract ODD POSITIVE FACTORS from it? From 36 = 2^2 * 3^2. Why can't we say that only EVEN prime factor is 2, with an exponent of 2 and adding 1 to the exponent, we get 2+1 = 3 EVEN factors ? This approach counts one combination that is NOT even (2⁰) but omits many combinations that ARE even (2*3, 2*3², etc.). A factor will be EVEN if its prime-factorization includes AT LEAST ONE 2. To directly count the EVEN positive factors of a positive integer, we could do the following: 1. Prime-factorize the integer. 2. Add 1 to every exponent OTHER THAN 2's exponent. 3. Multiply the results by 2's exponent. To illustrate: 720 = 2 * 3² * 5¹ The total number of EVEN factors = (4)(2+1)(1+1) = 24. The reason that we DON'T add 1 to 2's exponent is that an EVEN factor must include AT LEAST ONE 2, so 2⁰ is not an option. An even factor of 720 must include either 2¹, 2², 2³, or 2⁴. Thus, the total number of options with regard to 2⁴ is 4 -- the value of 2's exponent. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2527 messages Followed by: 353 members Upvotes: 1090 GMAT Score: 780 If you have the prime factorization of an even number, and it looks like this: (2^k) * some odd primes then the ratio of the number of even factors to the number of odd factors is k to 1. So if you take a number like: 120 = (2^3)(3)(5) then the ratio of even to odd divisors is 3 to 1, and so 3/4 of the factors of 120 will be even, and 1/4 of the factors of 120 will be odd. As a consequence, every even number has at least as many even divisors as odd divisors, and any multiple of 2^2 = 4 has at least twice as many even divisors as odd divisors. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com • Award-winning private GMAT tutoring Register now and save up to$200

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