Gcf Of 24 And 64

Introduction

In mathematics, the greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. The GCF is also known as the greatest common divisor (GCD). In this article, we will discuss how to find the GCF of 24 and 64.

Prime Factorization Method

One of the simplest methods to find the GCF of two numbers is the prime factorization method. In this method, we factorize each number into its prime factors and then find the common factors.

Prime Factors of 24

To find the prime factors of 24, we divide it by the smallest prime number, which is 2. We get 12 as the quotient and 0 as the remainder. So, we write 24 as 2 x 12. Similarly, we divide 12 by 2 and get 6 as the quotient and 0 as the remainder. So, we write 12 as 2 x 2 x 3. Therefore, the prime factorization of 24 is 2 x 2 x 2 x 3.

Prime Factors of 64

To find the prime factors of 64, we divide it by 2. We get 32 as the quotient and 0 as the remainder. So, we write 64 as 2 x 32. Similarly, we divide 32 by 2 and get 16 as the quotient and 0 as the remainder. So, we write 32 as 2 x 2 x 16. Continuing this process of dividing by 2, we get the prime factorization of 64 as 2 x 2 x 2 x 2 x 2 x 2.

Finding the GCF

To find the GCF of 24 and 64, we need to find the common factors in their prime factorizations. The common factors are the prime factors that are common to both numbers.

Common Factors of 24 and 64

The prime factors of 24 are 2 x 2 x 2 x 3 and the prime factors of 64 are 2 x 2 x 2 x 2 x 2 x 2. The common factors are the prime factors that are present in both factorizations. In this case, the common factors are 2 x 2 x 2, which is equal to 8.

Conclusion

In conclusion, the GCF of 24 and 64 is 8. We found it by using the prime factorization method, which involves factorizing each number into its prime factors and then finding the common factors. The GCF is an important concept in mathematics and is used in many applications, such as simplifying fractions and finding equivalent fractions.