Greatest Common Factor For 12 And 48

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Introduction

In mathematics, finding the greatest common factor (GCF) is an essential skill that every student should know. GCF is the highest number that can divide two or more integers without leaving any remainder. It is also known as the greatest common divisor (GCD). In this article, we will discuss how to find the GCF of 12 and 48.

Method 1: Prime Factorization

The first method to find the GCF of 12 and 48 is through prime factorization. Prime factorization is a process of breaking down a number into its prime factors. To do this, we need to find the prime factors of both 12 and 48. Prime factors of 12: 2 x 2 x 3 Prime factors of 48: 2 x 2 x 2 x 2 x 3 Then, we compare the common factors of both numbers, which are 2 and 3. We take the product of 2 and 3, which is 6. Therefore, the GCF of 12 and 48 is 6.

Method 2: Division Method

The second method to find the GCF of 12 and 48 is through the division method. The division method involves dividing the larger number by the smaller number and finding the remainder. Then, we divide the smaller number by the remainder and find the new remainder. We repeat this process until we get a remainder of zero. Let's apply this method to find the GCF of 12 and 48. 48 ÷ 12 = 4 with a remainder of 0 12 ÷ 4 = 3 with a remainder of 0 Therefore, the GCF of 12 and 48 is 4.

Conclusion

In conclusion, there are two methods to find the GCF of 12 and 48. The first method is through prime factorization, and the second method is through the division method. Both methods are effective, and it depends on the student's preference which method to use. It is essential to master this skill as it is often used in simplifying fractions and solving algebraic equations.