= 7 \times 13
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- Factor 78:
- = 2 \times 3 \times 13
- Factor 91:
- The only common prime factor is 13. Therefore, the GCF is:
- \]**Question:** A robotics engineer is programming a robot to navigate a rectangular grid. If the robot starts at the origin \((0,0)\) and moves to the point \((m,n)\) by only moving right or up, what is the number of distinct paths the robot can take? Express your answer in terms of \(m\) and \(n\).
- Solution:** The problem can be solved using combinatorics. The robot needs to make a total of \(m + n\) moves: \(m\) moves to the right and \(n\) moves up. The number of distinct paths is equivalent to the number of different ways to arrange these moves, which is given by the binomial coefficient:
