Prime Factorisation Method (HCF / GCD) at Algebra Den

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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.