Question

Describe, why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers?
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Answer 1

Answer:

1)7×11×13×13

2)7×6×5×4×3×2×1×5

1)7×11×13×13

ans:7×11×1(13)

7×11×13

77×13

1001

it is an composite number

2)7×6×5×4×3×2×1×5

ans:7×6×5×4×3×2×1×5

1×2×3×4×5×6×7×5

1×2×3×4×6×7×1(5)

1×2×3×4×5×6×7

2×12×20×42

24×840

20160

it is an composite number

Answer 2

Step-by-step explanation:

Given that:-

1)7×11×13+13

=>13(7×11+1)

=>13×(77+1)

=>13×(78)

=>13×2×39

=>13×2×3×13

=>2¹×3¹×13²

Given number is expressed as product of primes

by Fundamental theorem of arithmetic

given number is a composite number.

2)Given that:-

7×6×5×4×3×2×1+5

=>5(7×6×4×3×2×1+1)

=>5×(1008+1)

=>5×(1009)

=>5×1009

Given number is expressed as the product of primes

By Fundamental theorem of arithmetic

Given number is a composite number

Fundemental theorem of arithmetic:-

Every composite number can be expressed as product of primes and this prime factorization is unique apart from the order