Question

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

Answer 1

Hey mate, here is your answer.: -)

7×11×13+13

= 13 (7×11×1+1)

= 13 (7×11+1)

= 13 (77+1)

= 13×78

= 13×13×3×2

Since, it has more than two factors ... Hence, it is a composite number.. .



Now, 7×6×5×4×3×2×1+5

= 5 (7×6×1×4×3×2×1+1)

= 5 (7×6×4×3×2+1)

= 5 (1008+1)

= 5×1009×1

Since, it has more than two factors ... Hence, it is a composite number..

HOPE it helps to you!!!!

Answer 2

Step-by-step explanation:

• (i) 7 × 11 × 13 + 13

➲ 7 × 11 × 13 + 13

➲ ( 7 × 11 + 1) × 13

➲ (77 + 1) × 13

➲ 78 × 13

➲ 2 × 3 × 13 × 13

$\Huge\red{ Theorem \: :- }$

$\huge\bold\green{ ~֍~ }$ By $\tt\red{ Fundamental \: Theorem \: of \: Arithmetic }$

• Every $\tt\green{ composite \: number }$ can be expressed as the product of prime factor .

Here, 7 × 11 × 13 + 13 = 2 × 3 × 13 × 13

So, $\sf\orange{ 7 \: × \: 11 \: × \: 13 \: + \: 13 }$ is a $\sf\purple{ composite \: number }$

• (ii) 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

➲ 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

➲ 5040 + 5

➲ 5045

➲ 5 × 1009

✨ It is the product of prime factors ✨

$\huge\bold\pink{ ~֍~ }$ By $\tt\blue{ Fundamental \: Theorem \: of \: Arithmetic }$

• It is a $\sf\purple{ composite \: number }$

$\huge\colorbox{yellow}{ ~❊~ Divya ~❊~ }$