Question

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

Answer 1

Answer:

1st case

7*11*13+13 = 13(7*11+1) = 13*78 = 13*2*3*13

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

Similarly,

2nd case

7*6*5*4*3*2*1+5 = 5(7*6*4*3*2*1+1) = 5*1009

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

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

By the definition of composite number, we know, if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression;

7 × 11 × 13 + 13

Taking 13 as common factor, we get,

= 13(7×11×1+1) = 13(77+1) = 13×78 = 13×3×2×13

Hence,

• 7 × 11 × 13 + 13 is a composite number.

Now let’s take the other number,

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

Taking 5 as a common factor, we get,

= 5(7×6×4×3×2×1+1) = 5(1008+1) = 5×1009

Hence,

• 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.