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Ex 1.1, 6 Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Checking 7 × 11 × 13 + 13 7 × 11 × 13 + 13 = 13 × ( 7 × 11 + 1) = 13 × (77 + 1) = 13 × 78 = 13 × 13 × 3 × 2 Since it has more than two factors (13, 3, 2, 1, 13 × 78), ∴ It is a composite number Checking 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 Now, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 × (7 × 6 × 4 × 3 × 2 × 1 + 1) = 5 × (1008 + 1) = 5 × 1009 Since it has more than two factors (5, 1009, 1 , 5 × 1009), ∴ It is a composite number

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo