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Home » Shocking Diet Breakdown: What Do Hummingbirds Eating That You Don’t Know! - Abbey Badges

Shocking Diet Breakdown: What Do Hummingbirds Eating That You Don’t Know! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \boxed{78}

📌 Question: An ichthyologist notes that the population sizes of two fish species in a reef, $ a $ and $ b $, satisfy $ a + b = 1000 $, and both are divisible by the same prime number $ p $. What is the largest possible value of $ p $?

📌 We are given that $ a + b = 1000 $, and $ p \mid a $, $ p \mid b $, so $ p \mid (a + b) = 1000 $. Therefore, $ p $ must be a prime divisor of 1000.

📌 Factor 1000:

📌 = 2^3 \cdot 5^3

📌 So the prime divisors of 1000 are 2 and 5.

📌 The largest possible prime

📌 I’ll Become a Villainess Who Shatters Legends—History Will Fear Her Name!

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