i would say 25..
36^2 cab be written as 3^4* 2^4
hence the number of factors are (4+1) * (4+1) = 25..
let me know the OA.
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
factors
Source: Beat The GMAT — Problem Solving |
i understand this: 36^2 cab be written as 3^4* 2^4
but how do you go from there and arrive at the answer 25???
but how do you go from there and arrive at the answer 25???
There is rule to find the factors of any integer.
Suppose you need to find the number of factors for 20
First prime factorize
20 = 2*2*5 = 2^2 * 5^1
now just look at the exponents of two prime factors, you add 1 to each power and then multiply with each other
(2+1)*(1+1) = 3*2= 6
20 has 6 factors
1,2,4,5,10,20.
Similarly for 36^2 = 2^4 * 3^4
(4+1)*(4+1) = 5*5 =25
Hope its clear now.
Suppose you need to find the number of factors for 20
First prime factorize
20 = 2*2*5 = 2^2 * 5^1
now just look at the exponents of two prime factors, you add 1 to each power and then multiply with each other
(2+1)*(1+1) = 3*2= 6
20 has 6 factors
1,2,4,5,10,20.
Similarly for 36^2 = 2^4 * 3^4
(4+1)*(4+1) = 5*5 =25
Hope its clear now.
Great trick-thanks for that! Is there a similar trick if it were to ask for prime factors only?parallel_chase wrote:There is rule to find the factors of any integer.
Suppose you need to find the number of factors for 20
First prime factorize
20 = 2*2*5 = 2^2 * 5^1
now just look at the exponents of two prime factors, you add 1 to each power and then multiply with each other
(2+1)*(1+1) = 3*2= 6
20 has 6 factors
1,2,4,5,10,20.
Similarly for 36^2 = 2^4 * 3^4
(4+1)*(4+1) = 5*5 =25
Hope its clear now.
