How to calculate hcf

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how to calculate hcf

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How to calculate HCF (Highest Common Factor)

HCF, also known as the greatest common divisor (GCD), is the largest number that divides two or more given numbers without leaving a remainder. Calculating the HCF involves finding the common factors of the given numbers and determining the largest one.

Here are the steps to calculate the HCF:

  1. Prime Factorization Method:

    a. Start by decomposing each given number into its prime factors.

    b. Find the common factors among the prime factors of the given numbers.

    c. Multiply the common factors to find the HCF.

  2. Division Method:

    a. Write down the given numbers.

    b. Divide the larger number by the smaller number.

    c. Write down the remainder obtained.

    d. Replace the larger number with the smaller number and the smaller number with the remainder.

    e. Repeat steps b to d until the remainder becomes zero.

    f. The divisor in the last step is the HCF of the given numbers.

Let’s illustrate these methods with an example.

Example: Find the HCF of 24 and 36

Method 1: Prime Factorization Method

Step 1: Prime factorization of 24 = 2^3 * 3

Step 2: Prime factorization of 36 = 2^2 * 3^2

Step 3: Common factors = 2^2 * 3 = 12

Therefore, the HCF of 24 and 36 is 12.

Method 2: Division Method

Step 1: Write down the given numbers: 24, 36

Step 2: Divide the larger number by the smaller number: 36 ÷ 24 = 1 remainder 12

Step 3: Replace the larger number with the smaller number and the smaller number with the remainder: 24, 12

Step 4: Divide the new larger number by the new smaller number: 24 ÷ 12 = 2 remainder 0

Step 5: Since the remainder is zero, the divisor in the last step (12) is the HCF of the given numbers.

Therefore, the HCF of 24 and 36 is 12.

These methods can be used to calculate the HCF of any given numbers. Remember to choose the method that suits you best and practice solving different examples to become more proficient in calculating the HCF.