Question

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

Answer 1

Explanation:

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.