Algoritma Euclid

Algoritma Euclid adalah cara cepat untuk mendapatkan FPB (faktor persekutuan terbesar) dari sepasang bilangan bulat. Perhatikan contoh berikut :

FPB(18, 24) = FPB(18, 24−18) = FPB(18, 6) = FPB(18−6, 6) = FPB(12, 6) = FPB(12−6, 6) = FPB(6, 6).

Sehingga FPB dari 18 dan 24 adalah 6

Latihan

Tentukan :

(a) FPB (126, 24)

(b) FPB (1458, 441)

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Posted on April 4, 2012, in Matematika and tagged , , , , , . Bookmark the permalink. 1 Komentar.

  1. (a) FPB (126, 24) = FPB (126-24, 24) = FPB (102-24, 24) = FPB (78-24, 24) = FPB (54-24,

    24) FPB (30, 24) = FPB (30-24, 24) = FPB (6, 24-6) = FPB (6, 18-6) = FPB (6, 12-6) =

    FPB (6, 6) Jadi FPBnya adalah 6

    (b) FPB (1458, 441) = FPB (1458-441, 441) = FPB (1017-441, 441) = FPB (576-441, 441) = FPB (135, 441-135) = FPB (135,306-135 ) = FPB (135, 171-135) = FPB (135-36,36) = FPB (99-36,36) = FPB (63-36,36) = FPB (27,36-27) = FPB (27-9,9) = FPB (18-9,9) = FPB(9,9) Jadi FPBnya 9

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