Question

Q2: If two positive integers a and b are written as a=x?y? and b=xy, where x and y are prime numbers, then HCF(a,b) is (a) xy (b) xy? (c) xy (d) x?y?​

Answer 1

Answer:

HCF(Highestcommonfactor):−(AlsocalledasGCD)HCFoftwo

numbersisthenumberwhichcomletelydivides(with0remainder)

boththenumbers.Forexample,HCFof14and21is7,HCF(54,27)is27.

Givena=x

3

y

2

,b=xy

3

Itcanbeobservedthatxy

2

isacommonfactorofbothaandb.

HenceHCF(a,b)=xy

2

.