Calculate
Fraction 1
/
Fraction 2
/
Examples:
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.
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Tip: To simplify a fraction: divide numerator and denominator by their GCF. 48/18 → GCF=6 → 8/3 (fully simplified).
- 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)
GCF(48, 18)=648=2⁴×3, 18=2×3² → GCF=2×3=6
GCF(100, 75)=25100/25=4, 75/25=3, both exact
| Step | Calculation | Remainder |
|---|---|---|
| 1 | 48 = 2×18 + 12 | 12 |
| 2 | 18 = 1×12 + 6 | 6 |
| 3 | 12 = 2×6 + 0 | 0 → GCF = 6 |
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Fun Fact
The Euclidean algorithm (300 BCE) is one of the oldest algorithms still in use — over 2,300 years old. It is used in modern cryptography (RSA) to find modular inverses.
References
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