“Explain without much calculation how you know that 2, 3, 5, 7, 11, 13, and 17 are not factors of n = 2 · 3 · 5 · 7 · 11 · 13 · 17

Question

“Explain without much calculation how you know that 2, 3, 5, 7, 11, 13, and 17 are not factors of n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1.”

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Cherry 6 days 2022-12-31T11:28:45+00:00 1 Answer 0 views 0

Answer ( 1 )

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    2022-12-31T11:30:27+00:00
    2, 3, 5, 7, 11, 13, and 17 are not factors of n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1 because 1 is added to the product of the factors

    How to determine the factors?

    The product is given as:
    n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1
    Let 2 · 3 · 5 · 7 · 11 · 13 · 17 be represented by x.
    So, we have:
    n = x + 1
    Given the above equation.
    The factors of x cannot be the factors of n
    This is so because of the 1 that is added to x to given n
    Hence, 2, 3, 5, 7, 11, 13, and 17 are not factors of n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1 because 1 is added to the product of the factors
    Read more about factors at:
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