H.C.F. stands for Highest Common Factor.

The Highest Common Factor (H.C.F.) is a mathematical term used to describe the largest positive integer that divides two or more numbers without leaving a remainder. It is also known as the Greatest Common Divisor (GCD). The H.C.F. is commonly used in various mathematical operations, including simplifying fractions and finding the least common multiple (LCM).

How to find the H.C.F.?

To find the H.C.F. of two or more numbers, we can use different methods such as Prime Factorization, Division Method, and Euclidean Algorithm.

1. Prime Factorization Method:
- Step 1: Find the prime factors of each number.
- Step 2: Identify the common prime factors.
- Step 3: Multiply the common prime factors to find the H.C.F.

Example:
Let's find the H.C.F. of 12 and 18 using the prime factorization method.
- Step 1: The prime factors of 12 are 2 * 2 * 3.
- Step 2: The prime factors of 18 are 2 * 3 * 3.
- Step 3: The common prime factors are 2 and 3, so the H.C.F. is 2 * 3 = 6.

2. Division Method:
- Step 1: Divide the larger number by the smaller number.
- Step 2: Find the remainder.
- Step 3: Replace the larger number with the smaller number and the smaller number with the remainder.
- Step 4: Repeat steps 1-3 until the remainder is zero.
- Step 5: The last non-zero remainder is the H.C.F.

Example:
Let's find the H.C.F. of 32 and 48 using the division method.
- Step 1: 48 ÷ 32 = 1 remainder 16
- Step 2: 32 ÷ 16 = 2 remainder 0
- Step 3: The last non-zero remainder is 16, so the H.C.F. is 16.

3. Euclidean Algorithm:
- Step 1: Divide the larger number by the smaller number.
- Step 2: Find the remainder.
- Step 3: Replace the larger number with the smaller number and the smaller number with the remainder.
- Step 4: Repeat steps 1-3 until the remainder is zero.
- Step 5: The last non-zero remainder is the H.C.F.

Example:
Let's find the H.C.F. of 24 and 36 using the Euclidean algorithm.
- Step 1: 36 ÷ 24 = 1 remainder 12
- Step 2: 24 ÷ 12 = 2 remainder 0
- Step 3: The last non-zero remainder is 12, so the H.C.F. is 12.

Applications of H.C.F.
- Simplifying Fractions: The H.C.F. is used to simplify fractions by dividing both the numerator and denominator by their common factor.
- Finding the LCM: The H.C.F. is used to find the LCM by dividing the product of two numbers by their H.C.F.
- Dividing Objects

HIGHEST COMMON FACTOR