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Factors Of 48

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Unlocking the Secrets of 48: Understanding its Factors



Understanding factors is a fundamental concept in mathematics, crucial for grasping more advanced topics like prime factorization, fractions, and algebra. This article focuses on the factors of 48, a seemingly simple number that offers a great opportunity to explore this key mathematical idea. We will break down the process of finding factors, explain what they are, and show you how to apply this knowledge in various contexts.

What are Factors?



A factor of a number is a whole number that divides evenly into that number without leaving a remainder. In simpler terms, if you can divide a number by another number and get a whole number answer, then the number you divided by is a factor. For instance, 2 is a factor of 6 because 6 divided by 2 equals 3 (a whole number). Similarly, 3 is also a factor of 6.

Finding the Factors of 48: A Systematic Approach



There are several ways to find the factors of 48. Let's explore two effective methods:

1. The Pair Method: We systematically search for pairs of numbers that multiply to give 48. We start with 1, as 1 is a factor of every number:

1 x 48 = 48
2 x 24 = 48
3 x 16 = 48
4 x 12 = 48
6 x 8 = 48

Notice that we’ve progressed to larger numbers, and now if we continue, we’ll just repeat the same pairs (8 x 6, 12 x 4, etc.). This signifies we’ve found all the factors.

2. Prime Factorization: This method is particularly useful for larger numbers. Prime factorization involves breaking down a number into its prime factors (numbers divisible only by 1 and themselves). Let's do this for 48:

48 can be divided by 2: 48 = 2 x 24
24 can be divided by 2: 24 = 2 x 12
12 can be divided by 2: 12 = 2 x 6
6 can be divided by 2: 6 = 2 x 3

Therefore, the prime factorization of 48 is 2 x 2 x 2 x 2 x 3, or 2⁴ x 3. To find all the factors, we can combine these prime factors in different ways. For instance, 2 x 2 = 4 is a factor, 2 x 2 x 2 = 8 is a factor, and so on. This method ensures we don't miss any factors.

Listing All Factors of 48



Combining the results from both methods, we find the complete list of factors for 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Practical Applications of Finding Factors



Understanding factors is essential in various real-life situations:

Dividing objects evenly: If you have 48 candies and want to divide them equally among friends, knowing the factors helps you determine how many friends you can share with (1, 2, 3, 4, 6, 8, 12, 16, 24, or 48).
Simplifying fractions: To simplify the fraction 48/72, finding the greatest common factor (GCF) of 48 and 72 (which is 24) helps you reduce the fraction to its simplest form (2/3).
Solving algebraic equations: Factoring is a crucial step in solving many algebraic equations.

Key Insights and Takeaways



Finding factors is a fundamental skill in mathematics. The methods discussed – the pair method and prime factorization – provide efficient ways to determine all the factors of a number, no matter how large. Understanding factors allows you to solve various mathematical problems and apply this knowledge to real-world situations involving division, sharing, and simplification. Practice is key to mastering this concept; try finding the factors of other numbers to build your skills.


Frequently Asked Questions (FAQs)



1. What is the greatest common factor (GCF) of 48?
The greatest common factor of 48 is 48 itself, as it's the largest number that divides evenly into 48.

2. What is the least common multiple (LCM) of 48?
The least common multiple is the smallest number that is a multiple of 48. In this case, it’s 48.

3. Is 48 a prime number?
No, 48 is a composite number because it has more than two factors. Prime numbers only have two factors: 1 and themselves.

4. How many factors does 48 have?
48 has 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

5. Can negative numbers be factors?
While we typically focus on positive factors, it's worth noting that -1, -2, -3, -4, -6, -8, -12, -16, -24, and -48 are also factors of 48 because they divide evenly into 48. However, for many applications, we primarily focus on positive factors.

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How do you factor x^2-8x-48? - Socratic 5 Apr 2016 · x^2-8x-48=(x+4)(x-12) To factorize a polynomial of general form ax^2+bx+c, one should divide middle term bx in two parts, whose sum is b and product is axxc. So for x^2-8x-48, we should divide -8x in two parts which add up to -8 and whose product is 1xx(-48)=-48. A few trial indicate them to be -12 and 4.

What is the prime factorization of 48? | Homework.Study.com The prime factorization of 48 is 2 × 2 × 2 × 2 × 3. We can find the prime factorization of 48 using a factor tree. This...

What is the least common multiple of 48 and 12? - Socratic 5 Jul 2017 · 48 Factor each number into its prime factors: 48=2^4*3 12=2*3 Now, multiply each different factor, but only the ones with the highest exponent: lcm=2^4*3=48 The lowest common multiple is 48

Factors of 48x3? - Socratic The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 3 is a prime number. Prime numbers cannot be divided into a whole number that is greater than 1.

What are the factors of 48? - Homework.Study.com This means that the numbers 2 and 3 are factors of the number 6. Answer and Explanation: Every whole number has itself and 1 as factors, because 1 times any number gives you that number.

Do the following numbers share common factors? If so, which 29 Apr 2016 · Common factors are {1,2,3,4,6,8,12,16,24,48} and hence Greatest Common Factor is 48. Factors of 240 are {1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240 ...

What are the factor pairs of 48? | Homework.Study.com The factor pairs of the number 48 are: 1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8. When you multiply each of these factor pairs together, you get 48.... Become a member and unlock all Study Answers

How do you factor the expression x^2+14x+48? | Socratic 22 Jun 2018 · How do you factor the expression #x^2+14x+48#? Algebra Polynomials and Factoring Factorization of Quadratic Expressions. 1 Answer

What are the composite factors of 48? | Homework.Study.com The composite factors of 48 are 4, 6, 8, 12, 16, 24, and 48. These are composite factors because they are composite numbers themselves.

Express 48 as a product of its prime factors. Prime Factors: The 'factors' of a number are numbers which divide that number evenly. For example, the factors of 16 are 1, 2, 4, 8, and 16. The 'prime factors' of a number are the factors of the number which are also prime numbers. For 16, the only prime factor is 2.