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Home » If the sum of the first \( n \) positive integers is 210, find \( n \). - Aurero

If the sum of the first \( n \) positive integers is 210, find \( n \). - Aurero

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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v < \frac{67}{12} \approx 5.583
Since \( v \) is a positive integer, the largest possible value is \(...
4(5) + \frac{8}{3} = 20 + \frac{8}{3} = \frac{68}{3} \approx 22.67 < 2...
Try \( v = 6 \):
4(6) + \frac{8}{3} = 24 + \frac{8}{3} = \frac{72+8}{3} = \frac{80}{3}...
So \( v = 6 \) exceeds the limit. Thus, the maximum possible integer v...
Question:** What is the greatest common factor of 72 and 108?
We compute the prime factorizations:
= 2^3 \times 3^2, \quad 108 = 2^2 \times 3^3
The GCF is the product of the lowest powers of common primes:

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