Faktor Persekutuan 36 Dan 48: Cara Mencari & Contoh Soal

Oct 30, 2025 by Jhon Lennon 57 views

Faktor Persekutuan dari Bilangan 36 dan 48 Adalah

Okay, guys, let's dive into the world of numbers and figure out what the heck a common factor (or faktor persekutuan, as we say in Bahasa) is, especially when we're dealing with the numbers 36 and 48. It might sound intimidating, but trust me, it's easier than trying to assemble IKEA furniture without the instructions! We'll break it down step by step, so even if you're not a math whiz, you'll get the hang of it. So, what exactly is a common factor, and how do we find it for 36 and 48? Let's get started!

Memahami Apa Itu Faktor Persekutuan

Before we jump into the specifics of 36 and 48, let's make sure we're all on the same page about what a common factor actually is. Think of it like this: a factor is a number that divides evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because you can divide 12 by each of those numbers without getting a remainder. A common factor, then, is a number that divides evenly into two or more numbers. So, if we're looking for the common factors of 36 and 48, we want to find the numbers that can divide both 36 and 48 perfectly.

Why is this important? Well, common factors are used in all sorts of math problems, from simplifying fractions to solving algebraic equations. They're like the secret ingredient that makes everything work smoothly. Understanding common factors helps build a solid foundation for more advanced math concepts. Plus, it's just a neat trick to have up your sleeve! Now, let's get back to our main question: how do we actually find these common factors?

Mencari Faktor dari 36 dan 48

Alright, let's roll up our sleeves and get to work. The first step in finding the common factors of 36 and 48 is to list out all the factors of each number individually. This might seem a bit tedious, but it's the most straightforward way to make sure we don't miss anything. For 36, the factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. That's a fair few! Now, let's do the same for 48. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Okay, we've got our lists. What's next?

Now comes the fun part: comparing the two lists. We're looking for the numbers that appear in both lists. These are the common factors of 36 and 48. Take a close look. Do you see them? We've got 1, 2, 3, 4, 6, and 12. These are the numbers that divide evenly into both 36 and 48. So, the common factors of 36 and 48 are 1, 2, 3, 4, 6, and 12. See? Not so scary after all! You've officially found the faktor persekutuan of 36 and 48. High five!

Faktor Persekutuan Terbesar (FPB)

Now that we know all the common factors of 36 and 48, let's talk about a special one: the Faktor Persekutuan Terbesar, or FPB. In English, we call it the Greatest Common Factor (GCF). As the name suggests, the FPB is the largest of all the common factors. So, looking back at our list of common factors for 36 and 48 (1, 2, 3, 4, 6, and 12), which one is the biggest? That's right, it's 12!

Therefore, the FPB (or GCF) of 36 and 48 is 12. This is a super useful number because it's the biggest number that can divide both 36 and 48 without leaving a remainder. Finding the FPB is often used in simplifying fractions or solving problems where you need to divide things into equal groups. So, knowing how to find it is a valuable skill. How do you find the FPB? Simply identify all the common factors as we did earlier, and then pick out the largest one. Easy peasy!

Contoh Soal dan Pembahasan

To really solidify your understanding, let's work through a couple of example problems involving common factors. These examples will help you see how these concepts can be applied in different situations.

Contoh Soal 1:

Pak Budi has 36 apples and 48 oranges. He wants to divide them into identical baskets, with each basket containing the same number of apples and the same number of oranges. What is the maximum number of baskets Pak Budi can make?

Pembahasan:

This problem is a classic FPB application! The maximum number of baskets Pak Budi can make is equal to the FPB of 36 and 48, which we already know is 12. So, Pak Budi can make 12 baskets. Each basket will contain 36/12 = 3 apples and 48/12 = 4 oranges.

Contoh Soal 2:

Simplify the fraction 36/48.

Pembahasan:

To simplify a fraction, we need to divide both the numerator (36) and the denominator (48) by their greatest common factor. Again, we know that the FPB of 36 and 48 is 12. So, we divide both the top and bottom of the fraction by 12: 36/12 = 3 and 48/12 = 4. Therefore, the simplified fraction is 3/4.

Tips and Tricks

Finding common factors can be made even easier with a few handy tips and tricks. Here are a couple to keep in mind:

Start with Small Numbers: Always begin by checking if small numbers like 2, 3, 4, 5, and 6 are factors. These are often the easiest to identify.
Divisibility Rules: Knowing divisibility rules can save you a lot of time. For example, if a number is even, it's divisible by 2. If the sum of a number's digits is divisible by 3, the number itself is divisible by 3. And so on.
Prime Factorization: Another method for finding the FPB is to use prime factorization. Break down each number into its prime factors, and then identify the common prime factors. Multiply those common prime factors together, and you'll get the FPB.
Practice Makes Perfect: The more you practice finding common factors, the faster and more confident you'll become. Try working through various examples and problems.

Kesimpulan

So, there you have it! We've tackled the faktor persekutuan of 36 and 48 head-on. Remember, the common factors of 36 and 48 are 1, 2, 3, 4, 6, and 12, and their Faktor Persekutuan Terbesar (FPB) is 12. Understanding common factors is a fundamental skill in mathematics, and it opens the door to more advanced concepts. Keep practicing, and you'll be a math whiz in no time! You've got this, guys!