How many factors does 36^2 have?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

How many factors does 36^2 have?

by VJesus12 » Fri May 11, 2018 7:40 am

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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.

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Source: Beat The GMAT — Problem Solving | Fri May 11, 2018 7:40 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri May 11, 2018 7:49 am

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 - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 21, 2019 6:29 pm

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 factor'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

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