Question

5) explain why 7×11×101+11 is a composite number

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Answer 1

7×11×101+11=

11(7×101+1)

11(707+1)

11×708

11×2×2×3×59

7×11×101+11 has prime factorization Thus product of prime numbers is always composite number

Answer 2

$\sf {\underline{\underline{Answer :}}}$

$<b><u>Composite and Prime Numbers </u></b>$

${\underline {\texttt {Numbers are of two types :}}}$

$\texttt {1. Composite Numbers : The numbers having factors other than 1 and itself}$

$\texttt {2. Prime Numbers : The numbers that can be divided by 1 and itself}$

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$\sf {\underline {\underline {To\: Prove :}}}$

$\tt {7 \times 11 \times 101 + 1\: is\:a \:composite \: number }$

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$\sf {\underline {\underline {Solution :}}}$

$\tt {7 \times 11 \times 101 + 1 = 11 [( 7 \times 101) + 1]}$

$\tt {7 \times 11 \times 101 + 1 = 11 \times 708}$

$\texttt{The given expression has 11 and 708 as it's factors.}$ $\tt {\therefore\: it \:is \:a\: composite\: number.}$