A) use euclidean algorithm to find the greatest common divisor of 189 and 114? b) find a pair of integers x, y such that 189x + 114y = -6. c) find the prime number factorisation of 114. 2. [6 marks] a) express the continued fraction (2: 4, 1, 2) as a rational number. b) express the continued fraction -1; 2, 3,2 as a real number, where ** means a periodic repetition of ** 3. [6 marks] a) convert the 4-ary expansion 2.1301, into binary in simplest possible way (the efficiency of your solution will be taken into account). b) write (-21.231)s as a rational number in base 10. 4. [2 marks] what is god (2n + 1, 2n-1) for an integer n? (you must prove for your answer).