Question

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

Answer 1

Step-by-step explanation:

• The composite numbers are numbers which have more than 2 factors including the number itself and 1. For example- 4, 6, 8, 9, 12... are composite numbers.
• Numbers which have exactly 2 factors- 1 and the number itself, are known as prime numbers. For example- 2, 3, 5, 7, 11,...
• The number 1 has only one factor- 1. It has neither exactly 2 factors nor it has more than two factors. So, 1 is neither prime nor composite.

Coming back to the question ,

$7 \times 11 \times 13 + 13 = 13(7 \times 11 + 1) = 13(77 + 1) = 13 \times 78$

$7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5 = 5(7 \times 6 \times 4 \times 3 \times 2 \times 1 + 1) = 5(1008 + 1) = 5 \times 1009$

The above numbers could be expressed as product of two primes( or composite) , therefore these have more than two factors, so they are composite numbers.