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

As we know, for a number to be a composite number, it must have factors other than 1 and itself. ]

Thus, for the given expression;

7 × 11 × 13 + 13

It can be rewritten as,

=13(7 × 11 × 1 + 1) = 13(77 + 1) = 13 × 78 = 13 × 3 × 2 × 13

Since we have obtained 2 different factors, 7 × 11 × 13 + 13 is a composite number.

Now for the other expression,

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

It can be rewritten as,

=5(7 × 6 × 4 × 3 × 2 × 1 + 1) = 5(1008 + 1) = 5 × 1009

Since we have obtained 2 different factors, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.