We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
191
2
avatar+331 

Two integers are relatively prime if they have no common factors other than 1 or -1. What is the probability that a positive integer less than or equal to 30 is relatively prime to 30? Express your answer as a common fraction.

 Jul 8, 2018
 #1
avatar
-1

\( {7 \over 29}\)

.
 Jul 8, 2018
 #2
avatar
+1

Since 30 = 2 x 3 x 5, therefore it has common factors with the following numbers:
2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30[22 numbers]
It is relatively prime with following numbers:
1, 7, 11, 13, 17, 19, 23, 29[8 numbers]
Therefore, the probability that a number =< 30 is relatively prime to 30 is:
8 / 30 = 4 / 15

 Jul 8, 2018

5 Online Users