Q21. (2021) Explain why 2 × 3 × 5 + 5 and 5 × 7 × 11 + 7 × 5 are composite numbers.
Solution:1. Consider the first number: 2 × 3 × 5 + 5. – Factor out 5: 2 × 3 × 5 + 5 = 5(2 × 3 + 1) = 5(6 + 1) = 5 × 7 = 35. – Since 35 = 5 × 7 and both factors are greater than 1, 35 is composite.2. Consider the second number: 5 × 7 × 11 + 7 × 5. – Factor out 5 × 7: 5 × 7 × 11 + 7 × 5 = 5 × 7 (11 + 1) = 5 × 7 × 12 = 35 × 12. – Since 35 × 12 is a product of integers greater than 1, it is composite.Answer: Both numbers are composite because they can each be written as a product of integers greater than 1:- 2 × 3 × 5 + 5 = 5 × 7- 5 × 7 × 11 + 7 × 5 = 35 × 12
Explain why 2 × 3 × 5 + 5 and 5 × 7 × 11 + 7 × 5 are composite numbers.
