To find the greatest common divisor (GCD) of 48 and 256, we start by finding the prime factorizations of each number.

Wed, 06 May 2026 08:08:54 +0000

# Finding the Greatest Common Divisor (GCD) of 48 and 256: A Step-by-Step Guide When solving problems involving divisibility, one of the most essential concepts is the Greatest Common Divisor (GCD). The GCD of two numbers is the largest positive integer that divides both numbers without leaving a remainder. In this article, we’ll explore how to calculate the GCD of 48 and 256 using prime factorization — a clear and foundational method widely used in mathematics and computer science. ## Why Prime Factorization Matters for GCD Prime factorization breaks a number down into the fundamental building blocks of prime numbers. By comparing the prime factors of two numbers, we can easily identify the common factors and determine their greatest common divisor. This method offers strong insight into the mathematical structure and efficiency when dealing with larger numbers.