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Pengertian FPB dan KPK; Cara Mencari Faktor dan FPB; Menentukan FPB dengan Faktorisasi Prima; Latihan Soal Mencari FPB; Pengenalan Kelipatan Persekutuan Terkecil (KPK)

KPK dan FPB

Matematika

KPK dan FPB

Memahami dasar-dasar FPB dan KPK untuk pemecahan masalah.

Agenda

• Pengertian FPB dan KPK

• Cara Mencari Faktor dan FPB

• Menentukan FPB dengan Faktorisasi Prima

• Latihan Soal Mencari FPB

• Pengenalan Kelipatan Persekutuan Terkecil (KPK)

Apa Itu FPB dan KPK?

FPB adalah Faktor Persekutuan Terbesar, sedangkan KPK adalah Kelipatan Persekutuan Terkecil. Kita mempelajarinya untuk memecahkan masalah sehari-hari, seperti membagi kelompok atau mengatur jadwal. Mari kita pahami lebih lanjut!

Membagi objek alam: FPB dan KPK untuk masalah sehari-hari.

Memahami Faktor Persekutuan Terbesar (FPB)

FPB adalah bilangan bulat positif terbesar yang bisa membagi habis dua bilangan atau lebih tanpa sisa. Contohnya, FPB dari 12 dan 18 adalah 6, karena 6 adalah bilangan terbesar yang bisa membagi keduanya. Memahami FPB membantu kita menemukan faktor bersama yang paling besar.

Faktorkan x² + 7x + 12 menjadi (x + 3)(x + 4).

Mencari Faktor Suatu Bilangan

• Faktor adalah angka yang bisa membagi habis bilangan.

• Contoh: Faktor dari 12 adalah 1, 2, 3, 4, 6, 12.

• Cari pasangan perkalian yang hasilnya bilangan itu.

• Contoh: 1x12, 2x6, 3x4 untuk bilangan 12.

Menemukan Faktor Persekutuan

Faktor persekutuan adalah faktor-faktor yang sama dari dua atau lebih bilangan. Misalnya, faktor persekutuan dari 12 (1, 2, 3, 4, 6, 12) dan 18 (1, 2, 3, 6, 9, 18) adalah 1, 2, 3, dan 6. Untuk mencari Faktor Persekutuan Terbesar (FPB), kita pilih faktor persekutuan yang paling besar. Coba cari faktor persekutuan dari 20 dan 30!

Diagram lingkaran pecahan membantu memahami faktor persekutuan.

Anak fokus belajar perkalian, seperti dalam contoh faktor persekutuan.

Menentukan FPB dengan Mendaftar Faktor

• Tulis semua faktor bilangan pertama, contoh: 12 (1,2,3,4,6,12).

• Tulis semua faktor bilangan kedua, contoh: 18 (1,2,3,6,9,18).

• Lingkari faktor yang sama dari kedua bilangan (1,2,3,6).

• Pilih faktor persekutuan terbesar, yaitu 6.

Contoh FPB: 14 dan 35

Mari kita cari FPB dari bilangan 14 dan 35 dengan mendaftar faktornya. Faktor dari 14 adalah 1, 2, 7, dan 14. Sedangkan faktor dari 35 adalah 1, 5, 7, dan 35. Faktor persekutuan terbesar (FPB) dari 14 dan 35 adalah 7.

Faktor persekutuan dari 14 dan 35 adalah 7.

FPB 14 dan 35 adalah 7, menggunakan faktor persekutuan.

Mengenal Faktorisasi Prima

Faktorisasi prima adalah cara menuliskan sebuah bilangan sebagai perkalian dari bilangan-bilangan prima. Bilangan prima adalah bilangan yang hanya punya dua faktor, yaitu 1 dan bilangan itu sendiri, seperti 2, 3, 5, dan 7. Kita bisa menggunakan "pohon faktor" untuk mencari faktorisasi prima, contohnya faktorisasi prima dari 12 adalah 2 x 2 x 3.

Pohon faktor: faktorisasi prima dari 12 adalah 2 x 2 x 3.

Langkah FPB dengan Faktorisasi Prima

• Buat pohon faktor setiap bilangan.

• Tulis faktorisasi prima tiap bilangan.

• Pilih faktor prima yang sama.

• Ambil pangkat terkecil dari yang sama. Contoh: FPB 12 &amp; 18.

KPK dan FPB

Pengertian FPB dan KPK; Cara Mencari Faktor dan FPB; Menentukan FPB dengan Faktorisasi Prima; Latihan Soal Mencari FPB; Pengenalan Kelipatan Persekutuan Terkecil (KPK)

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