Question

Explain why 7 x 11 x 13+13 and 7 x 6 x 5 x 4 x 3 x2 x 1+5 are composite number.

Answer 1

Answer:

13(7×11×1+1)=13×78

this means that 7×11×23+13 is composite number as it has more than two factors i.e. 13 and 78

similarly we have to do in second case

Answer 2

$\bf\huge{\underline{\underline{Question}}}$

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

$\bf\huge{\underline{\underline{Solution}}}$

We have,

7 × 11 × 13 + 13 = 13[(7 × 11)+1] = 13[78]

i.e., 13 × 78 cannot be a prime number because it has factors 13 and 78.

∴ 13 × 78 is a composite number.

Also 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

⠀⠀= 5[7 × 6 × 4 × 3 × 2 × 1 + 1]

which is also not a prime number because it has a factor 5

Thus, 7 × 11 × 13 + 13 and ⠀⠀⠀⠀⠀⠀⠀⠀ 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.