Chapter 1: Real Numbers

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Q
Real Numbers Solutions

Question:

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers

Answer:

Proof: A composite number is a positive integer that has a factor other than 1 and itself.

 

If 7 × 11 × 13 + 13 may be written as 13  78. So other than 1 and the number itself, 13 and 78 are also the factors of the number. Further, 78= 39 x 2. So, 39 and 2 are also factors of 7 × 11 × 13 + 13. So this number is not a prime number. Hence its composite number.

Similarly, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 can be written as  5  1009. So, other than 1 and the number itself. 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 have also 5 and 1009 as factors. So it is also a composite number.

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