\text{GCD}(48, 72) = 2^3 \times 3 = 8 \times 3 = 24

Tue, 05 May 2026 12:41:41 +0000

# Understanding GCD(48, 72): How Prime Factorization Unlocks the Power of 24 When working with mathematical problems involving divisibility, one critical concept is the Greatest Common Divisor (GCD). In this article, we dive deep into the GCD of 48 and 72, revealing how prime factorization not only simplifies the problem but also demonstrates why GCD(48, 72) equals 24, not 8 × 3 = 24 — actually the same value expressed differently. ## What Is GCD? The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It’s foundational in number theory and proves essential in simplifying fractions, solving algebraic expressions, and working with modular arithmetic.