How do you find the GCF of two numbers?

The most efficient method is the Euclidean algorithm: divide the larger number by the smaller, then replace the larger with the smaller and the smaller with the remainder. Repeat until the remainder is 0. The last non-zero remainder is the GCF. Example: GCF(48, 18) → 48 = 2×18 + 12 → 18 = 1×12 + 6 → 12 = 2×6 + 0. GCF = 6.

When do you use GCF in real life?

GCF is used when simplifying fractions (divide numerator and denominator by GCF), splitting things into equal groups, distributing items evenly, and in algebra when factoring expressions. For example, to simplify 18/24: GCF(18,24) = 6, so 18/24 = 3/4.

What is the GCF of 12 and 18?

The GCF of 12 and 18 is 6. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors: 1, 2, 3, 6. The greatest is 6.

GCF Calculator – Greatest Common Factor of Any Numbers

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GCF Calculator FAQ

Common questions about the greatest common factor.

What is the GCF (Greatest Common Factor)?

The GCF is the largest number that divides evenly into two or more numbers with no remainder. It's also called the GCD (Greatest Common Divisor). For example, the GCF of 12 and 18 is 6 — the largest number that divides both exactly.

How do you find the GCF step by step?

Method 1 — List factors:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Largest common factor = 6

Method 2 — Euclidean algorithm (fastest):
GCF(48, 18): 48 = 2×18 + 12 → 18 = 1×12 + 6 → 12 = 2×6 + 0. GCF = 6

What is the difference between GCF and LCM?

GCF = largest number that divides into all the given numbers.
LCM = smallest number that all the given numbers divide into.

They're related: GCF(a,b) × LCM(a,b) = a × b. So if GCF(12,18)=6, then LCM = (12×18)/6 = 36.

When would two numbers have a GCF of 1?

When two numbers share no common factors other than 1, they are called coprime (or relatively prime). Examples: 7 and 13 (both prime), 8 and 15 (no shared prime factors). A fraction where numerator and denominator are coprime is already in its simplest form.

How is GCF used to simplify fractions?

Divide both the numerator and denominator by their GCF. Example: simplify 18/24.
GCF(18, 24) = 6
18 ÷ 6 = 3, 24 ÷ 6 = 4
18/24 = 3/4 (fully reduced)