Question

$(3 \times 11 \times 13 + 3)$ is :

• A. a prime number
• B. divisible by $13$
• C. a composite number
• D. an odd number

Hint:

Whenever you see a question of the form $a \times b \times c + c$, immediately factor out $c$:
$c \times (a \times b + 1)$.
Since this expresses the number as a product of two integers greater than 1, it must be a composite number.
This algebraic approach avoids tedious calculations and guarantees a correct result quickly.

Answer 1

The Correct Option is C

Step 1: Just multiply out the expression directly instead of factoring algebraically first.
\[ 3 \times 11 \times 13 + 3 \]
First multiply $3 \times 11 = 33$.
Then multiply $33 \times 13 = 429$.
Now add $3$:
\[ 429 + 3 = 432 \]

Step 2: Factor 432 directly to see how many divisors it has.
Break $432$ down step by step:
\[ 432 = 16 \times 27 \]
Since $16 = 2^4$ and $27 = 3^3$:
\[ 432 = 2^4 \times 3^3 \]

Step 3: Use this factorization to decide prime, composite, divisibility by 13, and odd/even, one at a time.
Since $432$ has prime factors other than itself and $1$ (namely $2$ and $3$, in multiple powers), it is not a prime number.
Since the factorization $2^4 \times 3^3$ contains no factor of $13$ at all, $432$ is not divisible by $13$.
Since $432$ ends in an even digit ($2$) and its factorization contains $2^4$, it is an even number, not an odd one.
Since $432$ has more than two positive divisors (for example $1, 2, 3, 4, 6, 8, \ldots, 432$), it is a composite number.

Final Answer:
The number $3 \times 11 \times 13 + 3 = 432$ is a composite number, which matches Option (C). \[ \boxed{432 = 2^4 \times 3^3 \text{ (composite)}} \]