To find the greatest common divisor (GCD) of 420 and 630, we start with their prime factorizations:

Thu, 16 Apr 2026 18:05:32 +0000

# Finding the Greatest Common Divisor (GCD) of 420 and 630: The Power of Prime Factorization Understanding the Greatest Common Divisor (GCD) is essential in mathematics, especially when working with fractions, ratios, and number theory. One commonly studied problem involves finding the GCD of two numbers—take 420 and 630, for example. These numbers appear frequently in real-world applications such as simplifying ratios, dividing resources evenly, or solving linear equations. In this article, we’ll explore how prime factorization makes finding the GCD straightforward and accurate. ## Why Prime Factorization? The GCD of two integers is the largest number that divides both without leaving a remainder. Prime factorization breaks each number into its fundamental building blocks—the prime numbers—which uniquely defines its divisors. By comparing the prime factors of 420 and 630, we identify the common ones and take the lowest power of each to determine the GCD.