Question

explain why 7×11×13+13 and 7×6×5×4×3×2×1+5are composite no​

Answer 1

Answer:

Step-by-step explanation:

As we know,

Compsite numbers are whole numbers that can be divided exactly by numbers other than 1 or itself.

For example 9 can be divided exactly by 3 (as well as 1 and 9), so 9 is a composite number.

Now 7×11×13+13= 1014. Since 1014 is divisible by numbers other than 1 and 1014 for eg it is divisible by 2,3 etc so it a composite number.

Again 7×6×5×4×3×2×1+5= 5045. Since 5045 is divisible by numbers other than 1 and itself for eg 5 etc. so it is a composite number.

Answer 2

Answer:

Here,

$\\ \tt \: (i) \: \: \: 7 \times 11 \times 13 + 13 = 13 \: (7 \times 11 + 1) \\ \\ \tt \: \: = 13 \times 78 = 13 \times 13 \times 2 \times 3 = 2 \times 3 \times {13}^{2}$

Factorisation of the number contains more than one prime.

$\\ \large{ \boxed{ \sf{ \therefore \: \: number \: \: is \: \: composite}}}$

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

Product of two numbers.

$\therefore\:\:$ It is not a prime.

$\therefore\:\:$ 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.