7Dr. Emily Carter identified fossil spores in three sediment layers: upper (18 samples), middle (42), lower (60). She wants to organize them into display cases such that each case has the same number of samples from each layer, with no samples left. What is the maximum number of display cases she can use?

7Dr. Emily Carter’s Discovery: Maximizing Display Cases with Equal Fossil Spore Samples from All Sediment Layers

In a groundbreaking study, paleontologist Dr. Emily Carter identified fossil spores in three distinct sediment layers from a key geological site: 18 samples from the upper layer, 42 from the middle layer, and 60 from the lower layer. These samples offer invaluable clues about ancient ecosystems and environmental changes across time. Now, Dr. Carter seeks to create equal, informative display cases for public engagement and research — each containing the same number of fossil spores from every sediment layer, with no samples left over. The challenge: what is the maximum number of display cases she can construct under these conditions?

Understanding the Context

Understanding the Problem

To ensure each display case has identical representation from all three layers, the number of samples from each layer per case must evenly divide the total counts: 18 upper, 42 middle, and 60 lower fossils. Thus, the critical question becomes: What is the largest number of cases such that each layer’s samples are fully and equally distributed?

This requires finding the greatest common divisor (GCD) of the three sample counts: 18, 42, and 60.

7Dr. Emily Carter identified fossil spores in three sediment layers: upper (18 samples), middle (42), lower (60). She wants to organize them into display cases such that each case has the same number of samples from each layer, with no samples left. What is the maximum number of display cases she can use?

Key Insights

Finding the Greatest Common Divisor (GCD)

We compute the GCD to determine the maximum number of display cases possible with no leftover samples:

Prime factorization:
- 18 = 2 × 3²
- 42 = 2 × 3 × 7
- 60 = 2² × 3 × 5

The common prime factors are 2 and 3, each to the lowest power present:

Minimum power of 2 = ²¹ → 2¹
Minimum power of 3 = ³¹ → 3¹

Thus:
GCD(18, 42, 60) = 2 × 3 = 6

🔗 Related Articles You Might Like:

📰 This Farmhouse Near You Is More Than Just Land—It’s estado alive 📰 Escape to the Quiet Farmlands Already Everyters Proclaim—La Granja Is Calling You Home 📰 the hidden power of the rare la herradura you’ve never been told about 📰 Shower Walk In Bath The Luxurious Wellness Routine Hot Right Now 📰 Shower Wall Tiles That Are Actually Worth The Splurge Shop Now 📰 Showmicks Mind Blowing Breakthrough Thats Taking The Internet By Storm 📰 Showtime Movie Secrets Revealed You Wont Believe What Happens In The Final Act 📰 Showtime Movie Sparks Jaw Dropping Emotional Cliffhanger That Wont Let You Look Away 📰 Shredded Beef Recipes That Are Simple Delicious And Absolutely Irresistible 📰 Shredded Beef Recipes That Save Time Perfect For Busy Home Chefs 📰 Shredded Beef Recipes Youll Never Want To Cook Againget These Today 📰 Shredders Revenge Exploded The Toxic Payback That Shocked The Online World 📰 Shredders Revenge How One Maser Attacked Back With An Unstoppable Machinery Assassin 📰 Shredders Revenge This Hidden Backlash Shocked Every Victim Now Theyre Raging 📰 Shredders Revenge Unleashed When Machines Turn Ugly This Cyber Vendetta Goes Viral 📰 Shrek Dragon The Surprising Truth Behind Their Legendary Partnership 📰 Shrek Characters Breaking Down Which One Spoils Your Progress 📰 Shrek Characters Unlocked The Hidden Secrets You Never Knew About Everyone

Final Thoughts

Organizing the Display Cases

Dr. Carter can therefore prepare 6 display cases — the maximum number possible — each containing:

18 ÷ 6 = 3 fossil spore samples from the upper layer
42 ÷ 6 = 7 fossil spore samples from the middle layer
60 ÷ 6 = 10 fossil spore samples from the lower layer

This balanced arrangement ensures each case is rich, consistent, and scientifically meaningful.

Why This Matters

By aligning her display strategy with mathematical precision, Dr. Carter not only honors scientific rigor but also enhances educational storytelling. Using the GCD to balance sample distribution ensures that each case delivers equal scientific value — a hallmark of thoughtful curation in paleontology.

Conclusion

The maximum number of display cases Dr. Emily Carter can create — with uniform, non-empty representation of fossil spores from all three sediment layers — is 6. This achievement reflects both scientific ingenuity and practical display planning, setting a powerful example for interdisciplinary research communication.