+0  
 
0
84
1
avatar+730 

The sum of two positive integers a and b is 80. What is the largest possible value of gcd(a,b)?

MIRB16  Jun 5, 2018
 #1
avatar+19813 
0

The sum of two positive integers a and b is 80. What is the largest possible value of gcd(a,b)?

 

\(\begin{array}{|r|r|r|r|} \hline a & b & a+b& gcd(a,b) \\ \hline 1&79&80&1 \\ 2&78&80&2 \\ 3&77&80&1 \\ 4&76&80&4 \\ 5&75&80&5 \\ 6&74&80&2 \\ 7&73&80&1 \\ 8&72&80&8 \\ 9&71&80&1 \\ 10&70&80&10 \\ 11&69&80&1 \\ 12&68&80&4 \\ 13&67&80&1 \\ 14&66&80&2 \\ 15&65&80&5 \\ 16&64&80&16 \\ 17&63&80&1 \\ 18&62&80&2 \\ 19&61&80&1 \\ 20&60&80&20 \\ 21&59&80&1 \\ 22&58&80&2 \\ 23&57&80&1 \\ 24&56&80&8 \\ 25&55&80&5 \\ 26&54&80&2 \\ 27&53&80&1 \\ 28&52&80&4 \\ 29&51&80&1 \\ 30&50&80&10 \\ 31&49&80&1 \\ 32&48&80&16 \\ 33&47&80&1 \\ 34&46&80&2 \\ 35&45&80&5 \\ 36&44&80&4 \\ 37&43&80&1 \\ 38&42&80&2 \\ 39&41&80&1 \\ 40&40&80&\color{red}40 \\ \hline \end{array}\)

 

The largest possible value of gcd(a,b) is 40

 

laugh

heureka  Jun 5, 2018

21 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.