What is the sum of the distinct prime factors of 360?
["What Is the Sum of the Distinct Prime Factors of 360?", "Understanding the prime factorization of a number helps unlock key insights into its mathematical properties—especially when exploring concepts like divisibility and number theory. One commonly asked question is: What is the sum of the distinct prime factors of 360? Let’s break it down clearly and deeply.", "### Understanding Prime Factors", "Prime factors are the prime numbers that multiply together to form a given composite number. Unlike repeated factors, distinct prime factors consider only unique primes.", "### Prime Factorization of 360", "To find the sum of the distinct prime factors of 360, start with its prime factorization:", "[\n360 = 2^3 \ imes 3^2 \ imes 5\n]", "In this decomposition:\n- The base primes are 2, 3, and 5\n- Each appears with an exponent (3, 2, and 1, respectively), but they are distinct due to different bases", "Thus, the distinct prime factors of 360 are 2, 3, and 5.", "### Calculating the Sum", "Now, simply add these unique primes:", "[\n2 + 3 + 5 = 10\n]", "### Why This Matters", "- Simplifies number analysis: Knowing distinct prime factors is crucial in cryptography, algorithm design, and even everyday math problems.\n- Foundational concept: Prime factors illustrate how complex numbers are built from simplest, indivisible units—prime numbers.\n- Real-world applications: The sum helps in identifying properties useful in computer science, such as checking for perfect numbers or solving modular arithmetic.", "### Conclusion", "The sum of the distinct prime factors of 360 equals 10. This result stems clearly from factoring 360 into (2^3 \ imes 3^2 \ imes 5), yielding the unique primes 2, 3, and 5—each fundamental to understanding the number’s structure.", "Keywords: sum of distinct prime factors, 360 prime factors, prime factorization 360, distinct primes, number theory explained"]
