Getting to Know Prime Factorization: Breaking Down 72

    Prime factorization can feel like a mystery puzzle, but it’s more like piecing together a delightful puzzle where every piece has its place. Let’s jump right into what makes 72 tick! To find its prime factorization, we first need to express 72 as a product of its prime factors. Now, don’t worry; this isn’t rocket science—it’s more like a treasure hunt with numbers. 

    So, what do we know about 72? Well, it’s an even number, and that already gives us a hint. Anytime you see an even number, you can kick things off by using 2, which is the smallest prime number. If we divide 72 by 2, we get 36. Who knew we’d find a friend along the way? But wait, we're not done yet!

    Let’s dive a little deeper. Now we need to factor 36 again. Divide 36 by 2, and you get 18. Divide 18 by 2, and voilà, we get 9. But here’s the twist: 9 isn’t even, so we switch gears. We can divide 9 by 3, the next prime number, and when we do that twice, we’re left with 1. 

    So, what’s our collection of primes as we broke down 72? We got three 2s (or \(2^3\)) and two 3s (or \(3^2\)). When we put it all together, we proudly display: 

    \(2 \times 2 \times 2 \times 3 \times 3\).

    That’s option C, which makes it the correct answer! Yeah, some might wonder why the other choices don’t fit. Remember option A? It mentions 38—definitely not a prime. And option B throws in a 19, which doesn’t belong in this factor party. Lastly, option D tries to sneak in 12, but sorry—a number must be prime or it needs to be broken down further, and 12 isn’t prime itself.

    Breaking down numbers can be a bit like finding your way through a maze. You keep peeling back layers, exploring new routes, and sometimes, you might hit a dead end. The trick is not to get discouraged—every route leads you closer to understanding. In today’s math world, being patient like this goes a long way.

    Understanding prime factorization doesn’t just assist you with basic algebra. It’s a stepping stone to more complex mathematical concepts, and let’s be honest—who doesn’t want to feel like a math wizard? When you can break down numbers effortlessly, you’re not just prepping for an exam; you’re crafting skills that will serve you well into higher learning.

    So, as you prepare for your College Algebra CLEP exam, don’t forget to practice breaking numbers down. From primes to composites, each number has a story to tell. You know what? Embrace the journey—it’s all part of your math adventure! Happy studying!