+0

# Two different natural numbers are selected from the set $\ \allowbreak \{1, 2, 3, \ldots, 6\}$. What is the probability that the greatest co

0
95
1
+136

Two different natural numbers are selected from the set $\ \allowbreak \{1, 2, 3, \ldots, 6\}$. What is the probability that the greatest common factor of these two numbers is one? Express your answer as a common fraction.

RektTheNoob  Sep 7, 2017

#1
+18715
+1

Two different natural numbers are selected from the set

$$\{1, 2, 3, \ldots, 6\}$$.

What is the probability that the greatest common factor of these two numbers is one?

$$\begin{array}{|r|r|r|r|} \hline n & & \text{greatest common factor } = 1 & \text{greatest common factor } \ne 1 \\ \hline 1. & 5,6 & 1 \\ \hline 2. & 4,6 & & 2 \\ 3. & 4,5 & 1 \\ \hline 4. & 3,6 & & 3 \\ 5. & 3,5 & 1 \\ 6. & 3,4 & 1 \\ \hline 7. & 2,6 & & 2 \\ 8. & 2,5 & 1 \\ 9. & 2,4 & & 2 \\ 10. & 2,3 & 1 \\ \hline 11. & 1,6 & 1 \\ 12. & 1,5 & 1 \\ 13. & 1,4 & 1 \\ 14. & 1,3 & 1 \\ 15. & 1,2 & 1 \\ \hline & sum & 11 \\ \hline \end{array}$$

The probability is $$\mathbf{\tfrac{11}{15}}$$

heureka  Sep 7, 2017
Sort:

#1
+18715
+1

Two different natural numbers are selected from the set

$$\{1, 2, 3, \ldots, 6\}$$.

What is the probability that the greatest common factor of these two numbers is one?

$$\begin{array}{|r|r|r|r|} \hline n & & \text{greatest common factor } = 1 & \text{greatest common factor } \ne 1 \\ \hline 1. & 5,6 & 1 \\ \hline 2. & 4,6 & & 2 \\ 3. & 4,5 & 1 \\ \hline 4. & 3,6 & & 3 \\ 5. & 3,5 & 1 \\ 6. & 3,4 & 1 \\ \hline 7. & 2,6 & & 2 \\ 8. & 2,5 & 1 \\ 9. & 2,4 & & 2 \\ 10. & 2,3 & 1 \\ \hline 11. & 1,6 & 1 \\ 12. & 1,5 & 1 \\ 13. & 1,4 & 1 \\ 14. & 1,3 & 1 \\ 15. & 1,2 & 1 \\ \hline & sum & 11 \\ \hline \end{array}$$

The probability is $$\mathbf{\tfrac{11}{15}}$$

heureka  Sep 7, 2017

### 6 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details