- (i) Use the Euclidean algorithm to find the highest common factor of 602 and 161.
Show each step of the algorithm.
(ii) The digits which can be used in a security code are the numbers \(1,2,3,4,5,6,7,8\) and 9.
Originally the code used consisted of two distinct odd digits, followed by three distinct even digits.
To enable more codes to be generated, a new system is devised. This uses two distinct even digits, followed by any three other distinct digits. No digits are repeated.
Find the increase in the number of possible codes which results from using the new system.