This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Find the prime factorization of each number. For 243: 243 = 3 × 81 81 = 3 × 27 27 = 3 × 9 9 = 3 × 3 So, the prime factorization of 243 is 3 × 3 × 3 × 3 × 3 = 3^5. For 145: 145 = 5 × 29 Both 5 and 29 are prime numbers. So, the prime factorization of 145 is 5 × 29. Step 2: Identify common prime factors. The prime factors of 243 are \3\. The prime factors of 145 are \5, 29\. There are no common prime factors between 243 and 145. Step 3: Determine the Greatest Common Divisor (GCD). Since there are no common prime factors, the greatest common divisor of 243 and 145 is 1. Alternatively, using the Euclidean algorithm: 243 = 1 · 145 + 98 145 = 1 · 98 + 47 98 = 2 · 47 + 4 47 = 11 · 4 + 3 4 = 1 · 3 + 1 3 = 3 · 1 + 0 The last non-zero remainder is 1. The Greatest Common Divisor (GCD) of 243 and 145 is 1.