3. What is the prime factorization of 84 ?

To get the prime factorization of 84, start by dividing it by the smallest prime number, which is 2. So, 84 ÷ 2 = 42. Next, divide 42 by 2 again to get 21. Now, 21 isn’t divisible by 2, but 3 is the next prime number. Dividing 21 by 3 gives you 7, which is also prime. Hence, the complete prime factorization of 84 is 2 × 2 × 3 × 7, or in exponential form, 2² × 3¹ × 7¹. Understanding the prime factorization of numbers like 84 can be super useful! For instance, it helps in simplifying fractions, finding the greatest common divisor (GCD), and even in cryptography! Plus, once you grasp the basics, you can tackle more complex numbers with confidence, unlocking a whole new level of math prowess. So, dive in and have fun with those factors!