Understanding Prime Factors: Digging into Elementary Math

When tackling elementary math, one common hurdle is understanding prime factors and their role in expressions. Don't worry! We’ll break it down together in a way that’s clear and approachable. Let’s dive into a specific problem: which expression has only prime factors of 3, 5, and 11?

We’re faced with four options:

A. 66 x 108
B. 15 x 99
C. 42 x 29
D. 28 x 350

You may be wondering: how do we figure this out? It’s all about breaking down these expressions into their prime factors. The answer, as we’ll see, is option B: 15 x 99. But let’s dig a bit deeper to understand why that’s the case.

First up, let’s tackle 15. It’s a number that breaks down nicely because it can be factored into 3 and 5. These are both prime numbers, which means they can’t be divided any further. Pretty straightforward, right?

Now, let’s break down 99. You might be surprised to learn that 99 can be expressed as 3 x 3 x 11 (or 3² x 11). With that in mind, when we combine the factors from both 15 and 99, we get the complete set: 3, 5, and 11. Bingo! This means 15 x 99 meets our criteria perfectly.

Now, you might be asking yourself, “What about the other options?” Great question! Let’s take a closer look.

For A. 66 x 108, when we factor these numbers, we find that 66 breaks down to 2 x 3 x 11, introducing that pesky factor of 2. That’s a no-go for our set of desired prime factors! As for 108, it breaks down into 2 x 2 x 3 x 3, which also includes 2. So, no luck there.

Moving on to C. 42 x 29. Looking at 42, it factors into 2 x 3 x 7. Ah, once again, we have that unwelcome factor of 2, which is not on our preferred list of 3, 5, and 11. And of course, 29 is prime but doesn’t belong to our set either—another strikeout.

Finally, we have D. 28 x 350. The number 28 breaks down into 2 x 2 x 7, which again brings in the factor of 2, and 350 factors into 2 x 5 x 7—which still has 2 knocking at our door.

To sum it all up: Option B—15 x 99—stands alone with 3, 5, and 11 as the only prime factors among the choices given. It's like having a clean, easy-to-read book in a library bustling with chaotic stacks of papers!

Understanding prime factorization doesn’t have to be intimidating. The beauty of math is that it’s often about finding patterns and connections. As you practice with more expressions, you’ll find your confidence growing.

So, next time you look at a math problem, remember this approach. Deconstruct your expressions and identify those prime factors—it’s like piecing together a puzzle! And who doesn’t love a good puzzle?

The key takeaway? Keep practicing and stay curious. With time, this will become second nature, making your study for subjects like the MTTC 103 Elementary Practice so much easier. Happy studying!