Question

Find the HCF and LCM using prime factorisation. A)396,1080 B)96,404 C)144,196

Answer 1

HCF and LCM using prime factorisation

A) 396, 1080

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$\begin{array}{r | l} 2 & 396 \\ \cline{1-2} 2 & 198 \\ \cline{1-2} 3 & 99 \\ \cline{1-2} 3 & 33 \\ \cline{1-2} 11 & 11 \\ \cline{1-2} & 1 \end{array}$

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$\begin{array}{r | l} 2 & 1080 \\ \cline{1-2} 2 & 540 \\ \cline{1-2} 2 & 270 \\ \cline{1-2} 3 & 135 \\ \cline{1-2} 3 & 45 \\ \cline{1-2} 3 & 15 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

• 396 = $\sf {\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times {\boxed{\sf{\red{3}}}} \times {\boxed{\sf{\green{3}}}} \times 11$

• 1080 = $\sf {\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times 2 \times {\boxed{\sf{\red{3}}}} \times {\boxed{\sf{\green{3}}}} \times 3 \times 5$

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Therefore, HCF of 396 and 1080 is,

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$:\implies\sf 2 \times 2 \times 3 \times 3$

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$:\implies\sf 4 \times 9$

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$:\implies{\underline{\boxed{\sf{\purple{36}}}}}\;\bigstar$

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$\begin{array}{r | l} 2 & 396, 1080 \\ \cline{1-2} 2 & 198, 540 \\ \cline{1-2} 3 & 99, 270 \\ \cline{1-2} 3 & 33, 90 \\ \cline{1-2} 3 & 11, 30 \\ \cline{1-2} 2 & 11, 10 \\ \cline{1-2} 11 & 11, 5 \\ \cline{1-2} 5 & 1, 5 \\ \cline{1-2} 1 & 1 \end{array}$

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$:\implies\sf 2 \times 2 \times 3 \times 3 \times 3 \times 2 \times 11 \times 5$

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$:\implies\sf 4 \times 9 \times 33 \times 5$

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$:\implies\sf 36 \times 165$

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$:\implies{\underline{\boxed{\sf{\pink{5940}}}}}\;\bigstar$

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B) 96, 404

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$\begin{array}{r | l} 2 & 96 \\ \cline{1-2} 2 & 48 \\ \cline{1-2} 2 & 24 \\ \cline{1-2} 2 & 12 \\ \cline{1-2} 2 & 6 \\ \cline{1-2} 3 & 3 \\ \cline{1-2} & 1 \end{array}$

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$\begin{array}{r | l} 2 & 404 \\ \cline{1-2} 2 & 202 \\ \cline{1-2} 101 & 101 \\ \cline{1-2} & 1 \end{array}$

• 96 = $\sf {\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times 2 \times 2 \times 2 \times 3$

• 404 = $\sf {\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times 101$

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Therefore, HCF of 96 and 404 is,

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$:\implies\sf 2 \times 2$

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$:\implies{\underline{\boxed{\sf{\purple{4}}}}}\;\bigstar$

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$\begin{array}{r | l} 2 & 96, 404 \\ \cline{1-2} 2 & 48, 202 \\ \cline{1-2} 2 & 24, 101 \\ \cline{1-2} 2 & 12, 101 \\ \cline{1-2} 2 & 6, 101 \\ \cline{1-2} 3 & 3, 101 \\ \cline{1-2} 101 & 1, 101 \\ \cline{1-2} & 1, 1 \end{array}$

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$:\implies\sf 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 101$

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$:\implies\sf 4 \times 8 \times 303$

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$:\implies\sf 32 \times 303$

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$:\implies{\underline{\boxed{\sf{\pink{9696}}}}}\;\bigstar$

━━━━━━━━━━━━━━━━━━━━━━

C) 144, 196

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$\begin{array}{r | l} 2 & 144 \\ \cline{1-2} 2 & 72 \\ \cline{1-2} 2 & 36 \\ \cline{1-2} 2 & 18 \\ \cline{1-2} 3 & 9\\ \cline{1-2} 3 & 3 \\ \cline{1-2} & 1 \end{array}$

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$\begin{array}{r | l} 2 & 196 \\ \cline{1-2} 2 & 98 \\ \cline{1-2} 2 & 46 \\ \cline{1-2} 23 & 23 \\ \cline{1-2} & 1 \end{array}$

• 144 = $\sf {\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times {\boxed{\sf{\red{2}}}} \times 2 \times 3 \times 3$

• 196 = $\sf {\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times {\boxed{\sf{\red{2}}}} \times 23$

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Therefore, HCF of 144 and 196 is,

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$:\implies\sf 2 \times 2 \times 2$

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$:\implies\sf 4 \times 2$

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$:\implies{\underline{\boxed{\sf{\purple{8}}}}}\;\bigstar$

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$\begin{array}{r | l} 2 & 144, 196 \\ \cline{1-2} 2 & 72, 98 \\ \cline{1-2} 2 & 36, 46 \\ \cline{1-2} 2 & 18, 23 \\ \cline{1-2} 3 & 9, 23 \\ \cline{1-2} 23 & 1, 23 \\ \cline{1-2} & 1, 1 \end{array}$

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$:\implies\sf 2 \times 2 \times 2 \times 2 \times 3 \times 23$

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$:\implies\sf 4 \times 4 \times 3 \times 23$

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$:\implies\sf 16 \times 3 \times 23$

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$:\implies\sf 48 \times 23$

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$:\implies{\underline{\boxed{\sf{\pink{1104}}}}}\;\bigstar$