\(HCF\) and \(LCM\) are widely used in number systems, especially in real numbers in finding relationship between different numbers and their general forms. A math teacher asked some questions related to \(HCF\) and \(LCM\) to his student.
1. If \(m\) and \(n\) are positive integer such that \(m=x^2y^3\) and \(n=xy^3\) where \(x\) and \(y\) are prime numbers then the \(HCF\) of \(m\) and \(n\) is
2. If \(LCM\) of \(408\) and \(170\) is \(2041\) then find \(HCF\)
3. Find the smallest number which leaves remainder \(8\) and \(12\) when divided by \(28\) and \(22\) respectively.
4. Find the greatest number which divides \(2011\) and \(2623\) leaving remainder \(9\) and \(5\) respectively.