Ex 1.1, 6 - Chapter 1 Class 10 Real Numbers

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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