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


7×11×13+13


Taking 13 as common, we get,


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


Taking 5 as common , we get,


= 5×(7×6×4×3×2×1+1)


= 5× (1008+1)


= 5×1009


1009 cannot be factorised further.


Therefore, the given expression has 5 and 1009 as its factors.


Hence, it is a composite number.


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