Question

4. Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x + x 3 x 2 x 1 + 5 are composite number
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Answer 1

7x11x13 + 13 = 13 x (7x11 + 1) = 13 x 78 = 13x13x6
Since it has more than two factors
So its a composite number

Similarly second part

Answer 2

Answer:

So, basically there are two types of numbers i.e., prime numbers and composite numbers. Understanding that, Prime numbers are those numbers having 1 and the number itself as factors. And, Composite numbers are those numbers having factors other than 1 and itself. It’s seen that, 7 x 11 x 13 + 13 = 13 x (7 x 11 + 1) [taking 13 out as common] = 13 x (77 + 1) = 13 x 78 = 13 x 13 x 6 So, the given expression has 6 and 13 as its factors. Therefore, we can conclude that it is a composite number. Similarly, 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = 5 x (7 x 6 x 4 x 3 x 2 x 1 + 1) [taking 5 out- common] = 5 x (1008 + 1) = 5 x 1009 Since, 1009 is a prime number the given expression has 5 and 1009 as its factors other than 1 and the number itself. Hence, it is also a composite number