What Is The Gcf Of 30 And 54?

GCF of 30 and 54 How to Find GCF of 30, 54? from www.cuemath.com

Introduction

In mathematics, the GCF or Greatest Common Factor is the largest positive integer that divides two or more numbers without leaving a remainder. In this article, we will discuss the GCF of 30 and 54 and provide a step-by-step solution to finding it.

Prime Factorization Method

One common method to find the GCF of two numbers is through prime factorization. Prime factorization is the process of breaking down a number into its prime factors. To find the GCF of 30 and 54 using prime factorization, we need to find the prime factors of both numbers.

Prime Factors of 30

To find the prime factors of 30, we can divide it by the smallest prime number, which is 2. Since 30 is even, it is divisible by 2. 30 ÷ 2 = 15 Since 15 is odd, we cannot divide it by 2. Therefore, we move to the next prime number, which is 3. 15 ÷ 3 = 5 5 is already a prime number, so we stop here. Therefore, the prime factors of 30 are 2, 3, and 5.

Prime Factors of 54

To find the prime factors of 54, we can also divide it by 2. 54 ÷ 2 = 27 27 is odd, so we divide it by 3. 27 ÷ 3 = 9 9 is divisible by 3. 9 ÷ 3 = 3 3 is already a prime number. Therefore, the prime factors of 54 are 2, 3, and 3.

Finding the GCF

To find the GCF of 30 and 54, we need to find the common factors of both numbers. Common factors are the factors that both numbers share. In this case, the common factors of 30 and 54 are 2 and 3. To find the GCF, we need to multiply the common factors together. 2 × 3 = 6 Therefore, the GCF of 30 and 54 is 6.

Conclusion

In conclusion, the GCF of 30 and 54 is 6. This was found by using the prime factorization method to find the prime factors of both numbers, and then finding the common factors and multiplying them together. The GCF is an important concept in mathematics, and it is often used in simplifying fractions and solving equations.