Explanation And Solution: What Is The Gcf Of 32 And 48?

List All the Factors of 32 From Least to Greatest from arelyfersleach.blogspot.com

Introduction

In mathematics, GCF stands for Greatest Common Factor. It is the largest number that divides two or more numbers exactly. In this article, we will discuss what is the GCF of 32 and 48.

Factors of 32 and 48

Before we find the GCF of 32 and 48, we need to determine the factors of each number. Factors are the numbers that can divide a particular number exactly without leaving any remainder. For 32, the factors are 1, 2, 4, 8, 16, and 32. For 48, the factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Common Factors of 32 and 48

Now that we know the factors of 32 and 48, we can determine their common factors. Common factors are the numbers that can divide both numbers exactly. The common factors of 32 and 48 are 1, 2, 4, 8, and 16.

Greatest Common Factor

Out of the common factors, the largest number is the GCF. Therefore, the GCF of 32 and 48 is 16.

Explanation of the Solution

To explain the solution further, we can use the prime factorization method. Prime factorization is the process of finding the prime factors of a number. The prime factors of 32 are 2 x 2 x 2 x 2 x 2, which can be written as 2^5. The prime factors of 48 are 2 x 2 x 2 x 2 x 3, which can be written as 2^4 x 3.

Common Prime Factors

To find the GCF using prime factorization, we need to identify the common prime factors of 32 and 48. The common prime factors are 2 x 2 x 2 x 2, which can be written as 2^4.

GCF using Common Prime Factors

Now that we have identified the common prime factors, we can find the GCF by multiplying them. Therefore, the GCF of 32 and 48 is 2^4, which is equal to 16.

Conclusion

In conclusion, the GCF of 32 and 48 is 16. We can find the GCF by determining the factors of each number, identifying the common factors, and selecting the largest common factor. Alternatively, we can use the prime factorization method to find the common prime factors and then multiply them to find the GCF.