Question

explain why 7 into 11 into 13 + 13 and 7 into 6 into 5 into 4 into 3 into 2 into 1 + 5 are composite numbers

Answer 1

7*11*13+13=13(7*11*1+1)

=13*78

=13*2*39

therefore it is a composite number as it has more than two factors

the second number can be proved using the same process

Answer 2

By the definition of composite number, we know, if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression;

7 × 11 × 13 + 13

Taking 13 as common factor, we get,

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

Hence, 7 × 11 × 13 + 13 is a composite number.

Now let’s take the other number,

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

Taking 5 as a common factor, we get,

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

Hence, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.