A rectangular field is 150 meters long and 80 meters wide. If the field is divided into square plots of the largest possible equal size, how many plots are there?

Sat, 18 Apr 2026 05:55:29 +0000

**A rectangular field is 150 meters long and 80 meters wide. If the field is divided into square plots of the largest possible equal size, how many plots are there?** Curious minds often wonder: when a space like this is segmented using the largest uniform square plots, how many can fit? This seemingly simple math problem taps into real-world applications in landscaping, farming, urban planning, and outdoor design—areas where precise land division drives productivity and value. In the US, where efficient land use is increasingly vital due to rising demand for open space, sustainable farming, and recreational areas, understanding optimal plot sizes helps stakeholders make informed, data-driven decisions. Under the surface, dividing a rectangle into equal square plots means finding the **largest square size** that evenly fits both dimensions. This relies on the greatest common divisor (GCD), the largest number that divides both length and width without remainders. For a 150-meter by 80-meter field, the GCD of 150 and 80 is 10 meters—meaning each square plot is 10m × 10m. Calculating plot count is straightforward:
- Length divided by plot side: 150 ÷ 10 = 15 plots
- Width divided by plot side: 80 ÷ 10 = 8 plots
- Total plots: 15 × 8 = **120**