Question: An industrial hygienist analyzing safety intervals finds that two protective protocols repeat every 15 and 25 days; what is the greatest common divisor of 15 and 25 to determine the longest consistent monitoring interval?

Thu, 30 Apr 2026 17:19:41 +0000

**An industrial hygienist analyzing safety intervals finds that two protective protocols repeat every 15 and 25 days; what is the greatest common divisor of 15 and 25 to determine the longest consistent monitoring interval?** In industrial workplaces where safety is paramount, understanding timing and alignment of protective measures shapes effective risk management. When two critical safety protocols reoccur at periodic intervals—every 15 and 25 days respectively—hygiene professionals must identify patterns that optimize monitoring without duplication or gaps. This question emerges increasingly in discussions around operational efficiency and compliance, as teams seek sustainable routines that balance vigilance with practicality. What mathematical insight can clarify the optimal cadence for overlapping safety checks? **Why This Pattern Matters in US Workplaces**
Recent trends in occupational health highlight a growing focus on data-driven scheduling to prevent workplace incidents. When two safety procedures repeat at different intervals, determining overlapping monitoring points helps avoid missed assessments. In US industries ranging from manufacturing to chemical processing, hygiene officers rely on clear intervals to ensure protocols are maintained consistently. The question about the greatest common divisor (GCD) arises naturally when evaluating how often both protocols coincide—and more importantly, how often a shared baseline interval offers the most effective monitoring cadence. **How the Greatest Common Divisor Defines Optimal Monitoring**
The GCD of two numbers identifies the largest interval that evenly divides both, revealing the longest repeating alignment. For 15 and 25, calculating the GCD means finding the largest integer that divides both numbers without remainder. Using prime factorization: 15 = 3 × 5 and 25 = 5², the only shared prime factor is 5. Thus, the GCD is 5. This means safety checks aligned every 5 days could serve as a consistent monitoring anchor, capturing both protocols’ effectiveness without overextending resources. This interval offers a practical balance—sufficiently frequent to maintain safety but spaced enough to remain manageable for human oversight.