HCF
HCF stands for highest common factor, the greatest positive integer that divides two or more integers without leaving a remainder. It is the same concept as the greatest common divisor (GCD).
HCF can be found by prime factorization or by the Euclidean algorithm. In prime factorization, write each
Examples illustrate the idea. For 48 and 18, gcd(48, 18) = 6, since 48 = 2^4 × 3 and
Properties include that the HCF is nonnegative and gcd(a,b) = gcd(b,a). Also gcd(a,0) = |a|, and gcd(0,0) is
Relation to other concepts: gcd(a,b) × lcm(a,b) = |a × b| for nonzero a and b, linking the