What is the prime factorisation of a = 43560? a=22.32.53.11 O a=2.33.52.112 O a=2.32.52.113 O a=22.32.5-113 O a=23.32.52.11 O a=23.32.5-112 What is the prime factorisation of b=24750? O b=2.32.53.11 O b=2.33.52.11 O b=2.3.53.112 O b=22.33.5-11 O b=22.3.5.113 O b=22.3.53.11 What are hof(a,b) and Icm(a,b)? Please write your answers as positive integers hof(a, b)= Icm(a,b)= (Liebeck, Chapter 11, Exercise 8a),b)) How many integer solutions do the Diophantine equations x -y and x2-x-y have? O x2=y3 has a unique solution at x=0,y=0 and x-x-y has infinitely many solutions. O x2-y3 has infinitely many solutions and x"-x=y has no solutions. O x2-y3 has no solutions and x2-x=y has infinitely many solutions x2=y3 has infinitely many solutions and x"-x=y' has two solutions at x=0,y=0 and x=1,y=0 x2=y3 has no solutions and x2-x=y' has a unique solution at x=0,y=0. O x2=y3 has a unique solution at x=0,y=0 and x"-x=y has no solutions