gcd of 120,288,360 is n(n+1)then n= ?
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Given GCD of 120,288,360 is n(n+1)
To find : n
Solution:
GCD Greatest common divisor or HCF Highest common factor
HCF = product of common factors of least power
120 = 2 * 2 * 2 * 3 * 5 = 2³ * 3¹ * 5¹
288 = 2 * 2 * 2 * 2 * 2 * 3 * 3 = 2⁵ * 3²
360 = 2 * 2 * 2 * 3 * 3 * 5 = 2³ * 3² * 5¹
GCD or HCF = 2³ * 3¹ = 24
n(n+1) = 24
=> n² + n - 24 = 0
=> n = (- 1 ± √(1 + 96) )/2
= (-1 ± √97)/2
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