Graduate Management Admission Test (GMAT) Practice Test

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What is the strategy for finding the greatest common factor (GCF) of two or more numbers?

divide and conquer
only using even numbers
list out prime factors; GCF is the product of common prime factors
subtract smallest from largest

The correct answer is: list out prime factors; GCF is the product of common prime factors

To find the greatest common factor (GCF) of two or more numbers, a sound strategy involves identifying the prime factors of each number and then determining which of these factors are common among all of the numbers. The GCF is then calculated as the product of these common prime factors. By listing the prime factors of each number, one can easily pinpoint those that appear in each number's factorization. For instance, if we take two numbers, say 30 and 45, the prime factorization of 30 is 2 × 3 × 5, and for 45, it's 3 × 3 × 5. The common prime factors here are 3 and 5, and their product, 15, is the GCF. This method is particularly effective because it relies on the fundamental principles of number theory, ensuring a thorough and correct assessment of all factors, especially in cases where numbers may be large or have multiple factors. It efficiently consolidates the process of finding the GCF without a trial and error approach, making it a reliable strategy for anyone seeking to solve such problems.