If two positive integers \\\\(a\\\\) and \\\\(b\\\\) are written as \\\\(a=x^2y^2\\\\) and \\\\(b=xy^2\\\\); \\\\(x\\\\), \\\\(y\\\\) are prime numbers then the \\\\(HCF(a,\\,b)\\\\) is
HCF by using the prime factorization method.Step1:\\\\(\ ext{Find the prime factorization of each of the number}\\\\)Step2:\\\\(\ ext{The product of all common prime factor is the HCF}\\\\)Here,\\\\(\\Rightarrow a=x\ imes x\ imes y\ imes y\\\\)\\\\(\\Rightarrow b=x\ imes y\ imes y\\\\)common Factors are \\\\(x\ imes y\ imes y\\\\)Thus ,\\\\(HCF(a,b)= xy^2\\\\)