The Greatest Common Factor Of 6 And 12: Explanation And Solution

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Introduction

The concept of finding the greatest common factor (GCF) is an essential skill in mathematics. It is used to find the largest number that divides two or more numbers without leaving a remainder. In this article, we will discuss the GCF of 6 and 12, its explanation, and solution.

What is GCF?

GCF stands for Greatest Common Factor, and it is the highest number that evenly divides two or more numbers. It is also known as the greatest common divisor (GCD) or highest common factor (HCF). The GCF of any two numbers is the largest number that can divide them both without leaving a remainder.

Explanation of GCF of 6 and 12

To find the GCF of 6 and 12, we need to list all the factors of both numbers. Factors are the numbers that divide another number without leaving a remainder. The factors of 6 are 1, 2, 3, and 6. The factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors of 6 and 12 are 1, 2, 3, and 6. The greatest common factor is the largest of these common factors, which is 6.

Solution

To find the GCF of 6 and 12, we need to list all the factors of both numbers and find the greatest common factor. Here are the steps to find the GCF of 6 and 12: Step 1: List all the factors of 6: 1, 2, 3, and 6. Step 2: List all the factors of 12: 1, 2, 3, 4, 6, and 12. Step 3: Identify the common factors of 6 and 12: 1, 2, 3, and 6. Step 4: The greatest common factor is 6. Therefore, the GCF of 6 and 12 is 6.

Why is GCF important?

The GCF is important in many areas of mathematics, including fractions, simplifying algebraic expressions, and finding the lowest common denominator. In fractions, the GCF is used to reduce the fraction to its lowest terms. In simplifying algebraic expressions, the GCF is used to factor out common terms. In finding the lowest common denominator, the GCF is used to determine the smallest multiple that two or more numbers have in common.

Conclusion

To sum it up, the GCF is the highest number that can divide two or more numbers without leaving a remainder. The GCF of 6 and 12 is 6, which is the largest number that can divide both 6 and 12 without leaving a remainder. The GCF is an essential skill in mathematics that is used in many areas of math, including fractions, simplifying algebraic expressions, and finding the lowest common denominator.