Question

Explain why 7x 11x 13+13and 7x6 x 5x4 x 3x 2x 1 +5 are composite numbers.​

Answer 1

$\large\bf{\underline{\underline{Consider}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\pink{\bigstar}★ \large\underline{\boxed{\bf\green{7 x 11 x 13 + 13}}}$

$\textbf\color{plum}{We can also write this as}$

$\sf{(77 + 1) x 13}$

$\color{red}\boxed{\sf{1014}}$

$\textbf\color{plum}{So the factors are}$

$\sf{13 x \:13 x \:3 x 2}$

$\small\color{lightpink}{It\: is \:a\: composite \:number.}$

$\textbf\color{plum}{The given number has more than two factors}$.

$\textit{Now \:consider}$

$\color{red}\boxed{\sf{7 x 6 x 5 x 4 x 3 x 2 x 1 + 5}}$

$\tt\color{darkgreen}{We\: can\: also\: write \:it \:as}$

$\color{red}\boxed{\sf{5(7 x 6 x 5 x 4 x 3 x 2 x 1 + 1)}}$

$\tt\color{darkgreen}{By\: calculation\: we\: get}$

$\large\bf{\underline{\underline{1009 x 5}}}$

It is a composite number. The given number has more than two factors.

$\underline{\bf{Hence\:proved.}}$

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Thankyou :)

Refer the attachment for better understanding :)