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Home >> H.C.F / G.C.D >> Successive Division Method >>

Successive Division Method (HCF / GCD)

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

 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 :- Step 1 = Divide the larger number 24 by the smaller number 18. And this division will give remainder 6. Step 2 = Now, divide 18 (divisor of step 1) with 6 (remainder of step 1) Step 3 = Division in Step 2 give us remainder 0(Zero). And The Last Divisor is the HCF of 24 & 18. Hence, HCF = 6              18 | 24 | 1                        18                       6 | 18 | 3                         18                 0               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 :- Step 1 = Divide the larger number 30 by the smaller number 20. And this division will give remainder 10. Step 2 = Now, divide 20 (divisor of step 1) with 10 (remainder of step 1) Step 3 = Division in Step 2 give us remainder 0(Zero). And The Last Divisor is the GCD of 20 & 30 = 10              20 | 30 | 1                               10 | 20 | 2                         20                 0               Phase 2 - Find the GCD of 10(GCD of 20 & 30) & 40(given number) :- Step 1 = Divide the remaining given number 40 by the GCD of 20 & 30 i.e.10. Step 2 = Division in Step 2 give us remainder 0(Zero). And The Last Divisor is the GCD of 10 & 40 = 10              10 | 40 | 4                        40           0           From Phase 1 & Phase 2, we concluded, GCD of 20, 30 & 40 = 10

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