Year 11 Maths - Specialist Number systems and sets

The Euclidean Algorithm

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Questions

Question 1

30035

Find HCF $\left( {720,425} \right)$

Answer

$5$

Worked Solution

$$
\begin{aligned}
720 &=1 \times 425+295 \\
425 &=1 \times 295+130 \\
295 &=2 \times 130+35 \\
130 &=3 \times 35+25 \\
35 &=1 \times 25+10 \\
25 &=2 \times 10+5 \\
10 &=2 \times 5+0 \\
H C F(5, 10)&=HCF(5,0) \\
\therefore\ HCF&=5
\end{aligned}
$$

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