Subject: Mathematics
Book: Maths Mastery
Also known as the Greatest Common Factor (GCF), the GCD of two numbers is the largest positive integer that divides them both without leaving a remainder. The standard method is the Euclidean Algorithm: if you want the GCD of 48 and 18, for instance, repeatedly apply gcd(a, b) = gcd(b, a mod b). With 48 and 18, 48 mod 18 = 12, so gcd(48, 18) = gcd(18, 12). Next, gcd(18, 12) = gcd(12, 6), and finally gcd(12, 6) = 6. So the GCD is 6. GCD calculations apply to simplifying fractions, finding common denominators, cryptography, and more. Mastering the Euclidean Algorithm also fosters efficiency in many integer-based math problems.
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