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Year 11 Maths - Specialist Number systems and sets

Natural numbers

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Questions
Question 1
30023

Find the highest common factor of 14280 and 6048.

\(168\)

$$\begin{align}
&\begin{aligned}
14280&=8 \times 1785 & 6048&=32 \times 189\\
&=8\times 5\times 357 & &=32 \times 27 \times 7\\
&=8 \times 5 \times 3 \times 119&
&=2^{5} \times 3^{3} \times 7\\
&=8 \times 5 \times 3 \times 7 \times 17&\\
&=2^{3} \times 5 \times 3 \times 7 \times 17&
\end{aligned}\\
&\therefore\quad HCF=2^{3} \times 3 \times 7=168
\end{align}
$$

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