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Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are …

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Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite number. (Real numbers)

    • Posted by Gomji Jaiswal 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Numbers are of two types - prime and composite.
    Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 and itself.
    It can be observed that
    7 × 11 × 13 + 13 = 13 × (7 × 11 + 1)
    = 13 × (77 + 1)= 13 × 78= 13 ×13 × 6
    The given expression has 6 and 13 as its factors.
    Therefore, it is a composite number.
    7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
    = 5 ×(7 × 6 × 4 × 3 × 2 × 1 + 1)
    = 5 × (1008 + 1)= 5 ×1009
    1009 cannot be factorized further
    Therefore, the given expression has 5 and 1009 as its factors.
    Hence, it is a composite number.

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