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Home >> H.C.F / G.C.D >> Prime Factorisation Method >>

## Prime Factorisation Method (HCF / GCD)

 Elucid's Division Lemma Method Prime Factorisation Method Successive Division Method

 Before you learn how to calculate HCF / GCD by Prime Factorisation Method, you must know What is Prime Factorisation ? Under Prime Factorisation Method, HCF / GCD = Product of Common Prime Factors. Following examples can guide you How to calculate HCF / GCD by Prime Factorisation Method ? Example = 1 By using Prime Factorisation Method, find the HCF of 24 & 18 ? Answer = Prime Factors of given numbers are as:- 24 = 2 × 2 × 2 × 3. 18 = 2 × 3       × 3. In the above prime factorisation, there are some common prime factors and these are underlined and written in bold letters. HCF = Product of Common Prime Factors.         = 2 × 3 = 6. Hence, HCF of 24 & 18 = 6 Example = 2 Find the GCD of 20, 30,& 40 by Prime Factorisation Method ? Answer = Prime Factors of given numbers are as:- 20 = 2 × 2       × 5. 30 = 2 × 3       × 5. 40 = 2 × 2 × 2 × 5. In the above prime factorisation, there are some common prime factors and these are underlined and written in bold letters. GCD = Product of Common Prime Factors.         = 2 × 5 = 10. Hence, GCD of 20, 30 & 40 = 10 Example = 3 Find the HCF of 28, 14 & 63 by Prime Factorisation Method ? Answer = Prime Factors of given numbers are as:- 28 = 2 × 2 × 7. 14 = 2       × 7. 42 = 2 × 3 × 7. In the above prime factorisation, there are some common prime factors and these are underlined and written in bold letters. HCF = Product of Common Prime Factors.         = 2 × 7 = 14. Hence, HCF of 28, 14 & 63 = 14.

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