Question

Which of the following is not a prime number

• A. 23
• B. 43
• C. 21
• D. 29

Hint:

Remember the divisibility test for 3: if the sum of a number's digits is divisible by 3, the number is divisible by 3.
For $21$: $2 + 1 = 3$, which is divisible by 3. Therefore, $21$ is composite and not prime.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In number theory, integers greater than 1 are classified into two categories:
1. Prime Numbers: Numbers that have exactly two distinct positive divisors: 1 and the number itself.
2. Composite Numbers: Numbers that have divisors other than 1 and themselves.

Step 2: Detailed Explanation:
Let us analyze each of the given options:
1. 23 (Option A):
Let us check for divisors.
The square root of $23$ is approximately $4.8$.
The prime numbers less than $4.8$ are $2$ and $3$.
Since $23$ is not divisible by $2$ or $3$, it is a prime number.
2. 43 (Option B):
The square root of $43$ is approximately $6.5$.
The prime numbers less than $6.5$ are $2, 3,$ and $5$.
Since $43$ is not divisible by $2, 3,$ or $5$, it is a prime number.
3. 21 (Option C):
Let us find the divisors of $21$.
The factors of $21$ are: \[ 21 = 1 \times 21 \] \[ 21 = 3 \times 7 \] Since $21$ has divisors ($3$ and $7$) other than 1 and itself, it is a composite number, not a prime number.
Therefore, this option is correct.
4. 29 (Option D):
The square root of $29$ is approximately $5.3$.
The prime numbers less than $5.3$ are $2, 3,$ and $5$.
Since $29$ is not divisible by $2, 3,$ or $5$, it is a prime number.

Step 3: Final Answer:
Among the options, 21 is not a prime number.
Therefore, the correct option is (C).