CLASS-6HIGHEST COMMON FACTOR (HCF)

HIGHEST COMMON FACTOR (HCF) -

The highest common factor (HCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more given positive integers without leaving a remainder. In other words, it is the largest number that divides all the given numbers.

For example, the HCF/GCD of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 evenly.

HCF/GCD is a fundamental concept in number theory and is often used in various mathematical and computational applications, such as simplifying fractions, finding equivalent fractions, and solving certain types of equations.

To find the HCF/GCD of two or more numbers, you can use methods like prime factorization, the Euclidean algorithm, or other advanced techniques depending on the context and the numbers involved.

The highest common factor (HCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more given positive integers without leaving a remainder. In other words, it's the greatest number that divides the given numbers evenly.

For example, let's find the HCF/GCD of two numbers, 12 and 18:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

The common factors of 12 and 18 are 1, 2, 3, and 6. Among these, the largest is 6. So, the HCF/GCD of 12 and 18 is 6.

HCF/GCD is a useful concept in mathematics and is often used in various applications like simplifying fractions, finding equivalent fractions, and solving problems related to ratios and proportions.

The highest common factor (HCF), also known as the greatest common divisor (GCD), of two or more integers is the largest positive integer that divides all the given numbers without leaving a remainder. In other words, it's the highest number that can evenly divide two or more numbers.

For example, let's find the HCF of two numbers, 24 and 36:

Factors of 24:- 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36:- 1, 2, 3, 4, 6, 9, 12, 18, 36.

The common factors of 24 and 36 are: 1, 2, 3, 4, 6, 12

The largest among these common factors is 12, so the HCF (GCD) of 24 and 36 is 12.

HCF (GCD) is an important concept in number theory and has various applications in mathematics and computer science, such as simplifying fractions, prime factorization, and modular arithmetic. It's commonly used to solve problems involving ratios, proportions, and divisibility.