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| Prime Factorisation Method (HCF / GCD) 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 (Topic already available in this site)
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 Factorisation 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 Factorisation 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 Factorisation 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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