Faktor Dari 48 Dan 60: Cara Menemukannya

Oct 31, 2025 by Jhon Lennon 41 views

Okay, guys, let's dive into finding the factors of 48 and 60. This is super useful in math, especially when you're dealing with simplifying fractions or understanding number relationships. Basically, when we talk about factors, we mean the numbers that divide evenly into another number. So, for example, the factors of 6 are 1, 2, 3, and 6 because 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 6 = 1. See? No remainders! Let's break down how to find the factors of 48 and 60 step-by-step.

Mencari Faktor dari 48

So, how do we actually find all the factors of 48? Well, start with the basics. We know that 1 and 48 are factors because every number is divisible by 1 and itself. Now, let's check if 2 is a factor. Yep, 48 is an even number, so 48 ÷ 2 = 24. That means 2 and 24 are a pair of factors. Next, let's try 3. 48 ÷ 3 = 16, so 3 and 16 are also factors. What about 4? Absolutely! 48 ÷ 4 = 12, so 4 and 12 are factors too. Keep going! Is 5 a factor? Nope, 48 ÷ 5 leaves a remainder. How about 6? Yes, indeed! 48 ÷ 6 = 8, making 6 and 8 factors. Now, here’s a cool trick: we've reached 6, and the next number to check would be 7, but since 8 is already in our list, and 6 x 8 gives us 48, we know we’ve found all the factors. So, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Easy peasy, right? Factoring 48 is useful because it shows all the different ways you can break down 48 into smaller whole number components. This is super useful in various mathematical applications, such as simplification, division, and finding common factors with other numbers.

Daftar Faktor dari 48:

Mencari Faktor dari 60

Alright, let's tackle 60 now. Just like with 48, we start with 1 and 60, because every number is divisible by 1 and itself. Is 2 a factor? You bet! 60 ÷ 2 = 30, so 2 and 30 are factors. What about 3? Yep, 60 ÷ 3 = 20, making 3 and 20 factors. How about 4? Absolutely! 60 ÷ 4 = 15, so 4 and 15 are factors too. Let's try 5. 60 ÷ 5 = 12, so 5 and 12 are factors. And finally, let's check 6. 60 ÷ 6 = 10, so 6 and 10 are factors. Now, just like before, we've reached a point where the next number (7) isn't a factor, and we've already found all the pairs up to the square root of 60. So, we know we've got all the factors. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Understanding the factors of 60 has practical applications. For example, if you’re dividing a group of 60 items into equal portions, knowing the factors tells you all the possible group sizes. If you had 60 cookies and you wanted to divide them equally among friends, you could divide them into groups of 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, or 60, allowing you to share fairly without cutting any cookies! This kind of factorization is essential in numerous everyday scenarios and mathematical problems.

Daftar Faktor dari 60:

Faktor Persekutuan dari 48 dan 60

Okay, now for the fun part: finding the common factors of 48 and 60. These are the numbers that are factors of both 48 and 60. We just list out the factors of each and see which ones they share. So, we know the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, and the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Let's compare these lists. Both lists include 1, 2, 3, 4, 6, and 12. So, the common factors of 48 and 60 are 1, 2, 3, 4, 6, and 12. Knowing these common factors is super important for simplifying fractions. Imagine you have a fraction like 48/60. To simplify it, you want to divide both the numerator (48) and the denominator (60) by a common factor. The biggest common factor is 12, so if you divide both by 12, you get 4/5. This is the simplest form of the fraction! Understanding common factors also helps in more complex mathematical problems, making calculations easier and more efficient. In addition to simplifying fractions, knowing the common factors helps in algebra and number theory, making this concept broadly applicable in a variety of contexts.

Daftar Faktor Persekutuan dari 48 dan 60:

Faktor Persekutuan Terbesar (FPB)

And finally, let's talk about the Greatest Common Factor (GCF), or Faktor Persekutuan Terbesar (FPB) in Indonesian. This is just the largest number that is a factor of both numbers. From our list of common factors, which are 1, 2, 3, 4, 6, and 12, the largest one is 12. So, the GCF of 48 and 60 is 12. Finding the GCF is extremely useful in simplifying fractions and in various other mathematical problems. For instance, if you’re trying to divide two different-sized groups into equal subgroups, the GCF tells you the largest possible size of those subgroups. If you have 48 apples and 60 oranges, and you want to make identical fruit baskets, the largest number of baskets you can make where each basket has the same number of apples and oranges is 12. Each basket would contain 4 apples (48 ÷ 12 = 4) and 5 oranges (60 ÷ 12 = 5). The concept of GCF extends beyond basic arithmetic; it's used in cryptography, computer science, and engineering. Understanding and calculating the GCF helps in optimizing algorithms, designing efficient systems, and solving real-world problems that involve dividing resources in the most effective way. So, nailing down how to find the GCF is a key skill in mathematics!

FPB dari 48 dan 60:

So there you have it! We've found the factors of 48, the factors of 60, their common factors, and their GCF. Keep practicing, and you'll become a factor-finding pro in no time!