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9 March, 09:57

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

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Answers (2)
  1. 9 March, 11:10
    0
    11∗13∗15∗17+17=17 (11∗13∗15∗1+1)

    11



    13



    15



    17

    +

    17

    =

    17

    (

    11



    13



    15



    1

    +

    1

    )

    Now, 11∗13∗15∗1

    11



    13



    15



    1

    is a product of odd numbers which is always odd.

    Thus, we have 17∗ (odd+1)

    17



    (

    o

    d

    d

    +

    1

    )

    =odd∗ (odd+odd)

    =

    o

    d

    d



    (

    o

    d

    d

    +

    o

    d

    d

    )

    =odd∗even

    =

    o

    d

    d



    e

    v

    e

    n

    =even

    =

    e

    v

    e

    n

    Now, 2 is the only prime number that is even. Hence, given number cannot be prime and is therefore composite
  2. 9 March, 13:44
    0
    Sol. We have, 7 x 11 x 13 + 13 = 1001 + 13 = 1014

    1014 = 2 x 3 x 13 * 13

    So, it is the product of more than two prime numbers. 2, 3 and 13.

    Hence, it is a composite number. 7 x 6x 5x 4 x 3 x 2 x 1 x 3 x 2 x 1 + 5 = 5040+5=5045

    5045 = 5 x 1009

    It is the product of prime factors 5 and 1009.

    Hence, it is a composite number.
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