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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
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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

heureka  Jun 5, 2018