How many of the integers in the collection {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} are relatively prime to 13?

waffles
Aug 23, 2017

#1**+1 **

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} are relatively prime to 13?

Since 13 is prime, they are all relatively prime to 13 except for 1

CPhill
Aug 23, 2017

#2**+1 **

**How many of the integers in the collection {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} are relatively prime to 13?**

Using the notation gcd(m,n) to denote the greatest common divisor, two integers and are relatively prime if **gcd(m,n) = 1**.

\(\begin{array}{|r|c|c|} \hline & \text{greatest common divisor} & \text{relatively prime} \\ \hline 1 & gcd(1,13) = 1 & \text{yes} \\ 2 & gcd(2,13) = 1 & \text{yes} \\ 3 & gcd(3,13) = 1 & \text{yes} \\ 4 & gcd(4,13) = 1 & \text{yes} \\ 5 & gcd(5,13) = 1 & \text{yes} \\ 6 & gcd(6,13) = 1 & \text{yes} \\ 7 & gcd(7,13) = 1 & \text{yes} \\ 8 & gcd(8,13) = 1 & \text{yes} \\ 9 & gcd(9,13) = 1 & \text{yes} \\ 10 & gcd(10,13) = 1 & \text{yes} \\ 11 & gcd(11,13) = 1 & \text{yes} \\ 12 & gcd(12,13) = 1 & \text{yes} \\ 13 & gcd(13,13) = 13 & \color{red}\text{no} \\ \hline \end{array}\)

heureka
Aug 23, 2017