Question

if two positive integers a and b are written as a=x4y2 and b=x3y where x and y are prime numbers find their HCF

Answer 1

Step-by-step explanation:

As a=x^2•y^2 = x*x*y*y

And b = x•y = x*y

As x and y are the prime no. Therefore both of them will definately not have any any other factor of them individually except 1 and the no. itself.

So, for all x and y HCF (a,b) = b = x•y

Example: take x=7, y= 11. ( both prime )

a=7*7*11*11 and b=7*11

Then surely: HCF (a,b) = 7*11

Extra: If we denie the condition of x and y being prime; even then we can say that the HCF (a,b) is for sure going to be 'b'. Because HCF is Highest Common Factor and as per the equations are.. in all cases HCF will be 'b'.

Example:

Say…. x=9, y=4

Then a=9*9*4*4 = 3*3*3*3*2*2*2*2

And b=9*4 = 3*3*2*2

HCF = 3*3*2*2 = 36