Jinsi ya kukokotoa GCF
GCF ni nini?
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest integer that divides two or more numbers exactly. Used in simplifying fractions, finding common denominators, and solving Diophantine equations.
Mwongozo wa Hatua kwa Hatua
- 1Prime factorization method: factor each number, take common prime factors with lowest powers
- 2Euclidean algorithm: GCF(a,b) = GCF(b, a mod b), repeat until remainder is 0
- 3GCF(a,b) × LCM(a,b) = a × b
- 4GCF of two primes is always 1 (they share no common factors)
Mifano Iliyotatuliwa
Ingizo
GCF(48, 18)
Matokeo
6
48=2⁴×3, 18=2×3² → GCF=2×3=6
Ingizo
GCF(100, 75)
Matokeo
25
100/25=4, 75/25=3, both exact
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