Question

Find the smallest positive integer x which is greater than 1 and relatively prime to 120 (recall that relatively prime means that the GCD of x and 120 is 1)

Answer 1

Answer: 7

Explanation:

List out the factors of 120 until we hit a gap

1,2,3,4,5,6,8

Note that 7 is not shown above. We can see that 120/7 = 17.14 approximately meaning that 7 doesn't go evenly into 120. So this is why 7 isn't a factor. Something like 3 is a factor because 120/3 = 40 is a whole number result.

Also, 7 is prime. The only factors of 7 are 1 and itself. This means that 7 and 120 do not have any common factors other than 1. The GCF of 7 and 120 is 1, leading to the two numbers being relatively prime

Side note: The term "coprime" is sometimes used in place of "relatively prime"