Which positive integers less than 12 are relatively prime to 12?

Solution:Step1To findWe have to find positive integers less than 12 are relatively prime to 12Step2A Prime Number can be divided uniformly only by 1, or itself. And it must be an entire number greater than 1. Relatively prime:-Two integers x and y are said to be relatively prime if the only positive integer that divides both of them is 1. For the relatively prime to 12 we have to find greatest common divisor(gcd) for all number which is less than 12 means 1,2,3,4,5,6,7,8,9,10,11.Nowgcd(1,12)=1gcd(2,12)gcd(3,12)gcd(4,12)gcd(5,12)=1gcd(6,12)gcd(7,12)=1gcd(8,12)=4gcd(9,12)=3gcd(10,12)=2gcd(11,12)=1Therefore, 1,5,7,11 are positive integers less than 12 are relatively prime to 12.