Question

Clare is making trail mix out of 14 bags of nuts and 18 bags of dried fruit. She wants each new portion of trail mix to be identical, containing the same combination of bags of nuts and bags of dried fruit, with no bags left over. What is the greatest number of portions of trail mix Clare can make?

Answer 1

\(\gcd(14, 18) = 2\)

\(14 = 2 \times 7\)
\(18 = 2 \times 9 \qquad [ = 2 \times 3^2]\)