HCF BY PRIME FACTORISATION METHOD

To find the Highest Common Factor (HCF) of two or more numbers using the prime factorization method, follow these steps: 

Step1: First, express each number as a product of its prime factors; 

Step 2: Then, identify the common prime factors of all the numbers; 

Step 3: find the lowest powers of common prime factors.

Step 4: Finally, calculate the HCF by multiplying the lowest powers of common prime factors. 

Example 1:

     Find the HCF of 48 and 72. 

1.          Step 1: Prime Factorization:

o                        48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

o                        72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²

2.        Step 2: Identify Common Prime Factors:

o                    Both numbers have 2 and 3 as prime factors.

3.        Step 3: Find the lowest Powers of common prime factors :

o                    For 2, the lowest power is 2³ (from 72's factorization)

o                   For 3, the lowest power is 3 (from 48's factorization)

4.        Step 4: Multiply the lowest Powers of Common prime factors:

o                HCF = 2³ x 3 = 8 x 3 = 24

 Therefore, the HCF of 48 and 72 is 24

Example 2:

    Find the HCF of 24, 36, 84.

    24=2 x 2 x 2 x 3 = 2³ x 3

    36= 2 x 2 x 3 x 3 = 2² x 3²

    84 = 2 x 2 x 3 x 7 = 2² x 3 x 7

    Common prime factors = 2, 3

    Lowest powers of common prime factors

    For 2 i.e. 2²

     For 3 i.e. 3

    HCF of 24, 36, 84 = 2² x 3

    Note

    👉 The HCF of given numbers is smaller than or equal to the smallest number among the given numbers.

    👉 HCF of two distinct prime numbers is 1.

    👉 HCF of two co-prime numbers is 1.

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