• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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 ## How many factors does 36^2 have? tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ### Top Member ## How many factors does 36^2 have? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult How many factors does 36^2 have? A. 2 B. 8 C. 24 D. 25 E. 26 The OA is the option D. How can I solve this question is a fast way? Can anyone give me a good explanation? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12991 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply VJesus12 wrote: How many factors does 36^2 have? A. 2 B. 8 C. 24 D. 25 E. 26 The OA is the option D. How can I solve this question is a fast way? Can anyone give me a good explanation? Thanks. -------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 ---NOW ONTO THE QUESTION----------------- 36 = (2)(2)(3)(3) So, 36Â² = (36)(36) = (2)(2)(3)(3)(2)(2)(3)(3) = (2^4)(3^4) So, the number of positive divisors of 36Â² = (4+1)(4+1) = (5)(5) = 25 Answer: D Cheers, Brent _________________ Brent Hanneson â€“ 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 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: 2811 messages Followed by: 18 members Upvotes: 43 VJesus12 wrote: How many factors does 36^2 have? A. 2 B. 8 C. 24 D. 25 E. 26 The approach here is to first find the prime factors of 36^2, and then add 1 to each prime factorâ€™s exponent and then find the product of those enhanced exponents. Thus, we have: 36^2 = (6^2)^2 = (2 x 3)^4 = 2^4 x 3^4 The total number of factors of 36^2 is (4 + 1)(4 + 1) = 5 x 5 = 25. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 49 first replies
2 Brent@GMATPrepNow 39 first replies
3 Jay@ManhattanReview 35 first replies
4 GMATGuruNY 29 first replies
5 ceilidh.erickson 14 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

206 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

82 posts
4 Ian Stewart

GMATiX Teacher

56 posts
5 GMATGuruNY

The Princeton Review Teacher

50 posts
See More Top Beat The GMAT Experts