5Donna purchased 3 types of rare plants for her greenhouse: 12 orchids, 18 ferns, and 24 succulents. She decides to arrange them in identical display groups, each containing the same number of each type of plant, with no plants left over. What is the greatest number of identical display groups she can create? - Treasure Valley Movers
5Donna purchased 3 types of rare plants for her greenhouse: 12 orchids, 18 ferns, and 24 succulents. She decides to arrange them in identical display groups, each containing the same number of each type, with no plants left over. What is the greatest number of identical display groups she can create?
5Donna purchased 3 types of rare plants for her greenhouse: 12 orchids, 18 ferns, and 24 succulents. She decides to arrange them in identical display groups, each containing the same number of each type, with no plants left over. What is the greatest number of identical display groups she can create?
In a growing trend among plant enthusiasts, smart organization drives both beauty and function—especially with rare, slow-growing specimens. When 5Donna purchased 12 orchids, 18 ferns, and 24 succulents for her greenhouse, her thoughtful challenge of grouping these plants efficiently sparked curiosity: What’s the largest number of identical displays she could make, each with equal numbers of every plant type? This is more than a gardening tactic—it’s a microcosm of resource harmony in natural collection.
Why This Question Is Rising in Greenhouse Communities
Understanding the Context
Recent digital conversations reveal increasing interest in creative, sustainable display methods among US gardeners. With urban green spaces becoming prized sanctuaries, efficient plant grouping enables aesthetic impact while preserving balance. For 5Donna, and many like her, arranging plants in equal groups supports thoughtful rotation, seasonal updates, and smarter space use—especially with unique, slow-growing specimens that command attention and care.
H3: The Math Behind the Ideal Grouping
To find the maximum identical groups with no leftovers, we calculate the greatest common divisor (GCD) of the plant counts: 12 orchids, 18 ferns, and 24 succulents. The GCD determines the highest number of uniform groups where each plant type divides evenly. Starting with prime factors:
Orchids: 12 = 2² × 3
Ferns: 18 = 2 × 3²
Succulents: 24 = 2³ × 3
The lowest power of shared primes: 2¹ and 3¹ give 2 × 3 = 6. Thus, the greatest number of identical display groups is 6—each holding 2 orchids, 3 ferns, and 4 succulents—fully utilizing all 60 plants.
Key Insights
H3: How to Create Balanced Display Groups
Arranging 12 orchids into 6 identical groups means 2 per group.
18 ferns divide into 3 per group (6 groups total).
24 succulents split evenly into 4 per group.
This alignment honors both botanical diversity and design uniformity, turning organic variety into intentional order. With each plant type balanced within every display, 5Donna doesn’t just organize flowers—she crafts living equations of balance.
