Question

find the hcf of 27 ,45,63​

Answer 1

$\mathfrak{\large{\underline{\underline{\red{Answer :-}}}}}$

HCF of 27 , 45 , 63 is 9

$\mathfrak{\large{\underline{\underline{\red{Explanation :-}}}}}$

$\textbf{Prime Factorization of 27}$

$\begin{array}{r|l} 3 & 27 \\\cline{1-2} 3 & 9 \\\cline{1-2} 3 & 3 \\ \cline{1-2} & 1 \end{array}$

$\textbf{Prime Factorization of 45}$

$\begin{array}{r|l} 3 & 45 \\\cline{1-2} 3 & 15 \\\cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

$\textbf{Prime Factorization of 63}$

$\begin{array}{r|l} 3 & 63 \\\cline{1-2} 3 & 21 \\\cline{1-2} 7 & 7 \\ \cline{1-2} & 1\end{array}$

$\implies$ 27 = 3 × 3 × 3

$\implies$ 45 = 3 × 3 × 5

$\implies$ 63 = 3 × 3 × 7

HCF = 3 × 3 = 9

$\therefore$ The Highest Common Factor of 27 , 45 , 63 is 9.

Answer 2

$\Large{\mathfrak{\underline{\underline{Answer :-}}}}$

HCF of 27, 45 and 63 is 9.

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$\Large{\mathfrak{\underline{\underline{Solution :-}}}}$

Prime Factorisation of 27 :

$\begin{array}{r|l} 3 & 27 \\ \cline{1-3} 3 & 9 \\ \cline{1-3} 3 & 3 \\ \cline{1-3} & 1 \end{array}$

Prime Factorisation of 45 :

$\begin{array}{r|l} 3 & 45 \\ \cline{1-3} 3 & 15 \\ \cline{1-3} 5 & 5 \\ \cline{1-3} & 1 \end{array}$

Prime Factorisation of 63 :

$\begin{array}{r|l} 3 & 63 \\ \cline{1-3} 3 & 21 \\ \cline{1-3} 7 & 7 \\ \cline{1-3} & 1 \end{array}$

27 = 3 × 3 × 3

45 = 3 × 3 × 5

63 = 3 × 3 × 7

HCF = 3 × 3

= 9

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