Question 6: Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
Explanatory Answer
i. 7 × 11 × 13 + 13
Taking 13 common, we can write the number as (7 × 11 + 1)13
= 78 × 13
78 × 13 is a product of 2 numbers, which is not of the form 1 × prime.
∴ 78 × 13 is composite.
ii. 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
Taking 5 common, we can write the number as (7 × 6 × 4 × 3 × 2 × 1 + 1)5
The above expression is a product of 2 numbers, which is not of the form 1 × prime.
Hence, the given number is a composite number.