Faktor Persekutuan 48 Dan 60: Cara Menghitungnya!

Oct 30, 2025 by Jhon Lennon 50 views

Okay, guys, let's dive into the world of numbers and figure out the faktor persekutuan (common factors) of 48 and 60. Don't worry, it's not as intimidating as it sounds! We'll break it down step by step, so you can become a pro at finding these common factors in no time. So, what exactly are we trying to find? Simply put, we want to identify all the numbers that can divide both 48 and 60 without leaving a remainder. These numbers are the common factors or faktor persekutuan that we're after.

Apa itu Faktor?

Before we jump into finding the faktor persekutuan of 48 and 60, let's quickly recap what factors are in general. A factor of a number is a whole number that divides evenly into that number, meaning there's no remainder left over. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 perfectly. Understanding factors is crucial because it forms the basis for finding faktor persekutuan. Think of it like this: factors are the building blocks of a number, and we want to find the blocks that 48 and 60 have in common. The process of finding factors usually involves systematically checking which numbers can divide the target number. This often starts with 1 and goes up to the number itself, although there are some shortcuts you can learn to speed up the process, especially when dealing with larger numbers. Now that we have a solid understanding of factors, we're well-equipped to tackle the main question: what are the faktor persekutuan of 48 and 60? Keep reading, and we'll find out!

Mencari Faktor dari 48

Okay, let's start by finding all the factors of 48. This means we need to find all the numbers that divide 48 evenly. We'll go through them systematically to make sure we don't miss any. Here we go:

1 is a factor of 48 because 48 ÷ 1 = 48
2 is a factor of 48 because 48 ÷ 2 = 24
3 is a factor of 48 because 48 ÷ 3 = 16
4 is a factor of 48 because 48 ÷ 4 = 12
6 is a factor of 48 because 48 ÷ 6 = 8
8 is a factor of 48 because 48 ÷ 8 = 6
12 is a factor of 48 because 48 ÷ 12 = 4
16 is a factor of 48 because 48 ÷ 16 = 3
24 is a factor of 48 because 48 ÷ 24 = 2
48 is a factor of 48 because 48 ÷ 48 = 1

So, the factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Make sure you write them all down! Having a clear list of factors for each number will make finding the common factors much easier. This is a foundational step, so take your time and double-check your work. Once you're confident that you've found all the factors of 48, we can move on to the next step: finding the factors of 60. By systematically identifying all the numbers that divide 48 without leaving a remainder, we've laid the groundwork for determining which of these numbers are also factors of 60. This process of breaking down a number into its factors is not only essential for finding faktor persekutuan but also for understanding other mathematical concepts like prime factorization and greatest common divisor (GCD). So, give yourself a pat on the back for mastering this step! Now, let's tackle finding the factors of 60.

Mencari Faktor dari 60

Alright, now let's find all the factors of 60. Just like we did with 48, we'll go through each number to see if it divides 60 evenly:

1 is a factor of 60 because 60 ÷ 1 = 60
2 is a factor of 60 because 60 ÷ 2 = 30
3 is a factor of 60 because 60 ÷ 3 = 20
4 is a factor of 60 because 60 ÷ 4 = 15
5 is a factor of 60 because 60 ÷ 5 = 12
6 is a factor of 60 because 60 ÷ 6 = 10
10 is a factor of 60 because 60 ÷ 10 = 6
12 is a factor of 60 because 60 ÷ 12 = 5
15 is a factor of 60 because 60 ÷ 15 = 4
20 is a factor of 60 because 60 ÷ 20 = 3
30 is a factor of 60 because 60 ÷ 30 = 2
60 is a factor of 60 because 60 ÷ 60 = 1

So, the factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Got them all written down? Great! Now we have a complete list of factors for both 48 and 60. This is where the magic happens! With these lists in hand, we can easily identify the numbers that appear in both lists, which are the faktor persekutuan we've been searching for. This step-by-step approach ensures that we don't miss any common factors. Finding the factors of 60 might seem a bit tedious, but it's a critical part of the process. By systematically checking each number, we can be confident that we've identified all the possible divisors of 60. Now that we have the factors of both 48 and 60, we're ready to move on to the exciting part: identifying the faktor persekutuan! So, keep your lists handy and get ready to compare. The next section will reveal the common factors of 48 and 60.

Menemukan Faktor Persekutuan

Okay, now for the grand finale! We have the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. And we have the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Now, let's see which numbers appear in both lists. These are our faktor persekutuan:

1 is a factor of both 48 and 60
2 is a factor of both 48 and 60
3 is a factor of both 48 and 60
4 is a factor of both 48 and 60
6 is a factor of both 48 and 60
12 is a factor of both 48 and 60

Therefore, the faktor persekutuan of 48 and 60 are: 1, 2, 3, 4, 6, and 12. Woo-hoo! We did it! This means that these numbers (1, 2, 3, 4, 6, and 12) can all divide both 48 and 60 without leaving any remainder. Understanding the faktor persekutuan can be super useful in various math problems, like simplifying fractions or solving problems involving ratios and proportions. By systematically identifying the factors of each number and then comparing the lists, we've successfully found the faktor persekutuan. This method can be applied to any pair of numbers. Remember, the key is to be organized and thorough in listing all the factors. This ensures that you don't miss any common factors. Now that you know how to find the faktor persekutuan, you can impress your friends and teachers with your math skills! Keep practicing, and you'll become a master of factors in no time. So, go ahead and try finding the faktor persekutuan of other pairs of numbers. You'll be amazed at how quickly you can solve these problems with a little practice.

Kesimpulan

So, there you have it! Finding the faktor persekutuan of 48 and 60 isn't so scary after all. Just remember to break it down into smaller steps: find the factors of each number individually, and then compare the lists to find the common ones. With a little practice, you'll be finding faktor persekutuan like a math whiz! Keep up the great work! Understanding faktor persekutuan opens the door to more advanced mathematical concepts. It's a foundational skill that will serve you well in various areas of math and problem-solving. So, don't underestimate the power of knowing your factors! Whether you're simplifying fractions, finding the greatest common divisor, or tackling more complex equations, the ability to identify faktor persekutuan will be invaluable. Keep exploring the world of numbers, and you'll discover endless patterns and relationships that make math fascinating. Now that you've mastered this concept, challenge yourself to find the faktor persekutuan of larger numbers or even sets of three or more numbers. The possibilities are endless! Remember, math is not just about memorizing formulas; it's about understanding the underlying principles and applying them creatively. So, embrace the challenge, have fun with numbers, and keep expanding your mathematical horizons. You've got this!