Ex 4) Find the prime factorization of 81

To find the prime factorization of 81, you start by dividing it by the smallest prime number, which is 3. Since 81 is divisible by 3, you can keep dividing: 81 ÷ 3 = 27, then 27 ÷ 3 = 9, and finally, 9 ÷ 3 = 3. You end up with three 3s multiplied together, followed by one last 3. Thus, the prime factorization of 81 is 3 × 3 × 3 × 3, or 3^4. In case you're wondering, prime factorization isn't just a textbook exercise; it has real-world applications, especially in cryptography and computer science! Many encryption algorithms rely on the difficulty of factoring large composite numbers into their prime components. So, the next time you're securing your online transactions, remember that prime factorization plays a crucial role in keeping your data safe!