ᴘᴇɴʏᴇʟᴇꜱᴀɪᴀɴ
Diketahui :
- 32, 36, 48
[tex] \: [/tex]
Ditanya :
- KPK ....?
[tex] \: [/tex]
Jawaban :
*Pohon faktor
[tex] \begin{gathered}\begin{aligned}& \: \: {\textsf{\textbf{32}}} \qquad \: {\textbf{\textsf{36}}} \qquad \: \textbf{\textsf{48}} \\ & \: \: \bigwedge \qquad \bigwedge \qquad \bigwedge \\ & \: {\sf{2 \: \: \: \: 16 \quad 2 \: \: \: 18 \quad 2 \: \: \: \: 24}} \\ & \quad \: \: \bigwedge \qquad \bigwedge \qquad \bigwedge \\ & \: \quad {\sf{2 \quad 8 \quad \: 2 \quad 9 \quad \: 2 \: \: \: \: 12}} \\ & \qquad \: \bigwedge \qquad \bigwedge \qquad \: \bigwedge \\ & \qquad {\sf{2 \quad 4 \quad \: 3 \quad 3 \quad \: \: \: 2 \quad 6}} \\ & \qquad \quad \bigwedge \qquad \qquad \quad \: \: \: \bigwedge \\ & \qquad \: \: \: {\sf{2 \quad 2 \qquad \qquad \quad 2 \quad 3}} \end{aligned}\end{gathered} [/tex]
[tex] \: [/tex]
*Faktorisasi prima
32 = 2⁵
36 = 2² × 3²
48 = 2⁴ × 3
[tex] \: [/tex]
KPK = 2⁵ × 3²
KPK = (2 × 2 × 2 × 2 × 2) × (3 × 3)
KPK = 32 × 9
KPK = 288
[tex] \: [/tex]
ᴋᴇꜱɪᴍᴘᴜʟᴀɴ
Jadi, KPK dari 32, 36, 48 adalah 288
Jawaban:
Faktorisasi prima dari 32 = 2^5
Faktorisasi prima dari 36 = 2² x 3²
Faktorisasi prima dari 48 = 2^4 x 3
KPKnya = 2^5 x 3² = 32 x 9 = 288
