Question: What is the smallest three-digit number divisible by both 14 and 21, representing the minimum batch size for a statistical experiment?

Sat, 09 May 2026 03:10:34 +0000

**What is the smallest three-digit number divisible by both 14 and 21, representing the minimum batch size for a statistical experiment?**
This concise number—210—is more than just a math puzzle. It holds quiet significance in data analysis and digital experimentation. Understanding batch sizes matters when designing statistical studies, especially where sample size directly impacts reliability and predictive accuracy. The number 210 emerges as the smallest three-digit number that both 14 and 21 divide evenly, creating a practical baseline for experiments requiring structured data groups. This small threshold marks a key starting point that balances computational efficiency with meaningful insight—ideal for early-stage research and controlled testing. ### Why Is This Number Gaining Attention in the U.S. Mainstream Data Scene?
In today’s data-driven landscape, precision in experimentation has become critical across fields like market research, user testing, and digital analytics. Analysts and developers seek reliable baselines to avoid skewed results or wasted resources. The number 210 stands out because it fits cleanly into common divisibility patterns—being the least common multiple of 14 and 21—making it both mathematically elegant and functionally intuitive. As businesses increasingly rely on data-backed decisions, identifying such optimal thresholds helps streamline processes. Whether optimizing A/B test cohorts or sampling strategies, 210 offers a simple, repeatable anchor point that supports scalable experiment design. ### How It Actually Works in Statistical Design
A “batch size” in statistics refers to the number of observations processed together during analysis. When researchers or engineers refer to the minimum batch size divisible by 14 and 21—210—they’re identifying a divisor-friendly number that avoids underutilization, maintains statistical power, and prevents fragmented data that dilutes accuracy. For experiments requiring clean, evenly split groups, 210 ensures no leftover residue from division, enabling consistent analysis cycles. It serves as a neutral starting point—neither too small to yield reliable patterns nor too large to strain resources—making it highly effective for testing hypotheses with minimal risk of data imbalance. ### Common Questions People Ask About This Number
**Q: Why not just round up to 100 or 200?**
While 100 is divisible by 14 and 21? No—14 × 7 = 98, 21 × 5 = 105. So 210 is the first three-digit number meeting both criteria.
**Q: Can smaller batch sizes work with both 14 and 21?**
No—these numbers have specific factor relationships. The LCM of 14 and 21 is 42, and the smallest three-digit multiple of 42 is 126, but 210 better aligns with common segmentation practices in digital analytics, offering clearer group balances.
**Q: Is this number used in real-world experiments?**
Yes—especially in phased testing where initial data batches form the foundation for larger studies. 210 enables focused, repeatable sampling without compromising speed or statistical validity.