Math, asked by abiaaabid7777, 17 days ago

Explain why 7 × 11 × 13 + 13 is a composite Number .​

Answers

Answered by BrainlyMrKing
308

To Explain :-

Why 7 × 11 × 13 + 13 is a composite Number .

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For Solving the question we must know the 2 concepts , Let's understand the concepts first :-

Concept 1 :-

Product of Prime and Composite Number is always a Composite Number . To understand better let's take a example :- 2 [ Prime Number ] × 4 [ Composite Number ] = 8 [ Composite Number ]

Concept 2 :-

"Fundamental Theorem of Arithmetic" which says Every Composite number can be expressed as the product of prime factors and Prime factorisation is unique except the oder . Let's take an example :-

12 [ Composite Number ] = 2 × 2 × 3

Here we expressed 12 [ composite number ] as product of prime factors , it's unique because if anyone in the world will express 12 as prime factors will get either 2 × 2 × 3 or 3 × 2 × 2 or 2 × 3 ×2 just oder will be different . Let's now proceed to our solution !!

Solution :-

 \sf \longrightarrow 7 \times 11 \times 13 + 13

As 7 × 11 × 13 is one term and 13 is another term , Therfore taking 13 as common

 \longrightarrow \sf 13 (7 \times 11 + 1)

 \longrightarrow \sf 13 (77 + 1)

 \longrightarrow \sf {{{  {{{{\red{\sf{\sf 13(78)}}}}}}}}} \: is \: a \: composite \: number

Here concept 1 will be used which is Product of prime and Composite is a composite Number ∴ 13 [ Prime Number ] × 78 [ Composite Number ] = Composite Number . So , 7 × 11 × 13 + 13 is a composite Number . If u want u can solve it upto here also but we can extend our solution too :-

Taking Prime factors of 78 ,

\begin{gathered}{\begin{array}{ c|c}2&78 \\ \hline 3&39  \\ \hline 13&13 \\ \hline &1\end{array}} \qquad \therefore 78 = 2 \times 3 \times 13\end{gathered}

 \longrightarrow \sf 13 (2 \times 3 \times 13)

 \longrightarrow \sf {{{  {{{{\red{\sf{\sf 13  \times 2 \times 3 \times 13 }}}}}}}}}

Here our 2nd Concept is used , As "Fundamental Theorem of Arithmetic" says Every composite Number can be expressed as Product of prime numbers ∴ 13 × 2 × 2 × 13 are product of prime numbers . So , 7 × 11 × 13 + 13 is a composite Number .

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Aryan0123: Awesome!
Answered by llPRINCESSSOFIAll
48

Answer:

Given 7×11×13+13

=13×(7×11+1)=3×78 

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

similarly in

7×6×5×4×3 ×2×1+5   

=5(7×6×4×3 ×2×1+1)=5×1009   

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

hope it will help you

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