LCM AND HCF

LCM AND HCF
H.C.F by using prime factorisation
Finding the Highest Common Factor (HCF) using prime factorization involves expressing each number as a product of its prime factors and then identifying the common prime factors. Here's a step-by-step guide:
Step 1: Prime Factorization
    Prime factorization of 24: 2³×3¹(because 2×2×2×3=24)
    Prime factorization of 36: 2²×3²(because 2×2×3×3=36
Step 2: Identify Common Prime Factors
    The common prime factors are 2²×3^{1
Step 3: Multiply Common Prime Factors
    Multiply the common prime factors to get the HCF:
    HCF =} 2²×3^{1 = 4 x 3 = 1
Step 4: Result
    The HCF of 24 and 36 is 12.
    This method is quite efficient for finding the HCF, especially when dealing with larger numbers, as it focuses on the prime factors directly
Let's find the HCF of 24 and 36 as an example.
    Express each of the given number as the product of their prime factors. The product of the least powers of the common factors gives the H.C.F of the given numbers
Example - I: Find the H.C.F of 360 and 756 by using prime factorisation method
   
    360 = 23 x 32 x 5        
    756 = 22 x 33 x 7 
    clearley the common  factors are 2 and 3 
    H.C.f =least power of 2 x least power of 3 
        = =4 x 9=36
    Hence, H.C.F of 360 and 756 is 36.}