Calculating HCF / GCD by Prime Factorisation Method is long and more time-consuming, and due to these disadvantages new method was evolved by Mathematician namely, Successive Division Method
Under Successive Division Method, HCF / GCD = The Last Divisor of the given numbers .
Following examples can guide you How to calculate HCF / GCD by Successive Division Method ?
Example = 1 By using Successive Division Method, find the HCF of 24 & 18 ?
Answer = Steps and the way of finding HCF by Successive Division Method is as :-
18 | 24 | 1 Step 1 = Divide the larger number 24 by the smaller number 18. And this division will give remainder 6.
18
6 | 18 | 3 Step 2 = Now, divide 18 (divisior of step 1) with 6 (remainder of step 1)
18
0 Step 3 = Division in Step 2 give us remainder 0(Zero). And The Last Divisor is the HCF of 24 & 18. Hence, HCF = 6
Example = 2 Find the GCD of 20, 30,& 40 by Successive Division Method ?
Answer = As here three numbers are given, so it involves Two Phases.
Phase 1 - Find the GCD of 20 & 30 :-
20 | 30 | 1 Step 1 = Divide the larger number 30 by the smaller number 20. And this division will give remainder 10.
20
10 | 20 | 2 Step 2 = Now, divide 20 (divisior of step 1) with 10 (remainder of step 1)
20
0 Step 3 = Division in Step 2 give us remainder 0(Zero). And The Last Divisor is the GCD of 20 & 30 = 10
Phase 2 - Find the GCD of 10(GCD of 20 & 30) & 40(given number) :-
10 | 40 | 4 Step 1 = Divide the remaining given number 40 by the GCD of 20 & 30 i.e.20.
40
0 Step 2 = Division in Step 2 give us remainder 0(Zero). And The Last Divisor is the GCD of 10 & 40 = 10
From Phase 1 & Phase 2, we concluded, GCD of 20, 30 & 40 = 10
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