GRE Quantitative Arithmetic Mastery Hub: The Industry Founda

According to "The Complete GRE Number Properties & Integers Course 2026: From Zero to Expert!", which of the following statements about prime factorization is MOST crucial for solving problems involving the greatest common divisor (GCD) of two large integers without explicit computation of their prime factors?

In the context of "The Complete GRE Number Properties & Integers Course 2026: From Zero to Expert!", how does the concept of modular arithmetic, specifically congruences, provide an elegant shortcut for determining the last digit of a large power of an integer, even when direct calculation is infeasible?

"The Complete GRE Number Properties & Integers Course 2026: From Zero to Expert!" emphasizes the importance of understanding divisibility rules. When faced with a large integer $N$ and asked to determine if it's divisible by 7, which of the following applications of number properties offers the most robust and universally applicable method, superior to simple trial division?