Explain why 7 × 11 × 13 + 13 is a composite Number .
Answers
To Explain :-
✧ Why 7 × 11 × 13 + 13 is a composite Number .
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 :-
As 7 × 11 × 13 is one term and 13 is another term , Therfore taking 13 as common
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 ,
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 .
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