How many factors does 36^2 have?

This topic has expert replies
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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

User avatar
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, 36² = (36)(36)
= (2)(2)(3)(3)(2)(2)(3)(3)
= (2^4)(3^4)
So, the number of positive divisors of 36² = (4+1)(4+1)
= (5)(5)
= 25

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage