The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. It represents the highest factor that is common to all the given numbers.
The concept of the Highest Common Factor involves the following knowledge points:
The HCF of two or more numbers can be calculated using the prime factorization method. The formula for finding the HCF is:
HCF(a, b) = Product of common prime factors of a and b
To find the HCF using the formula, follow these steps:
The symbol for the Highest Common Factor is "HCF" or "GCD" (Greatest Common Divisor).
There are several methods to find the HCF:
Example 1: Find the HCF of 24 and 36.
Solution: Step 1: Prime factorization of 24 = 2^3 * 3 Step 2: Prime factorization of 36 = 2^2 * 3^2 Step 3: Common prime factors = 2^2 * 3 = 12 HCF(24, 36) = 12
Example 2: Find the HCF of 45, 60, and 75.
Solution: Step 1: Prime factorization of 45 = 3^2 * 5 Step 2: Prime factorization of 60 = 2^2 * 3 * 5 Step 3: Prime factorization of 75 = 3 * 5^2 Step 4: Common prime factors = 3 * 5 = 15 HCF(45, 60, 75) = 15
Question: What is the highest common factor? Answer: The highest common factor, also known as the greatest common divisor, is the largest positive integer that divides two or more numbers without leaving a remainder. It represents the highest factor that is common to all the given numbers.