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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
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\( {7 \over 29}\)

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 Jul 8, 2018
 #2
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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

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