Prime Number Identification: Select the Prime from Given Options

Q: Why is 2 the only even prime number?

Because all other even numbers are divisible by 2! Since 2 itself is only divisible by 1 and 2, it's prime. But 4, 6, 8, 10... are all divisible by 2, so they have more than two factors.

Q: How do I quickly check if a small number is prime?

For numbers under 10, just check if they're divisible by 2 or 3. The primes less than 10 are: 2, 3, 5, 7. Everything else (4, 6, 8, 9) has other factors.

Q: Is there a pattern to prime numbers?

Not really! Primes become more spread out as numbers get larger, but there's no simple formula. That's what makes them so interesting in mathematics!

Q: What's the easiest way to remember what makes a number prime?

Think of it as "picky numbers" - they only allow exactly two factors to divide them evenly: 1 and themselves. If any other number divides evenly, it's not prime!

Q: Can negative numbers be prime?

No, by definition prime numbers are positive. We only consider positive integers greater than 1 when talking about primes.

Prime Number Identification with Small Integers

Choose the prime number from the options.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the prime number from the options.

Step-by-step solution

To solve this problem, we'll check each number to determine if it's a prime:

Number 6: Greater than 1 but divisible by 2 and 3. Not prime.
Number 4: Greater than 1 but divisible by 2. Not prime.
Number 8: Greater than 1 but divisible by 2 and 4. Not prime.
Number 2: Greater than 1 and not divisible by any other numbers except 1 and itself. It is prime.

Therefore, the prime number from the options is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime numbers have exactly two factors: 1 and themselves
Method: Check divisibility by numbers less than itself (6÷2=3)
Verification: List all factors to confirm only 1 and the number itself ✓

Common Mistakes

Avoid these frequent errors

Thinking 1 is a prime number
Don't count 1 as prime = wrong classification! By definition, prime numbers must have exactly two distinct factors, but 1 only has one factor (itself). Always remember that prime numbers start from 2.

Practice Quiz

Test your knowledge with interactive questions

Which of the numbers is a prime number?

FAQ

Everything you need to know about this question

Why is 2 the only even prime number?

Because all other even numbers are divisible by 2! Since 2 itself is only divisible by 1 and 2, it's prime. But 4, 6, 8, 10... are all divisible by 2, so they have more than two factors.

How do I quickly check if a small number is prime?

For numbers under 10, just check if they're divisible by 2 or 3. The primes less than 10 are: 2, 3, 5, 7. Everything else (4, 6, 8, 9) has other factors.

Is there a pattern to prime numbers?

Not really! Primes become more spread out as numbers get larger, but there's no simple formula. That's what makes them so interesting in mathematics!

What's the easiest way to remember what makes a number prime?

Think of it as "picky numbers" - they only allow exactly two factors to divide them evenly: 1 and themselves. If any other number divides evenly, it's not prime!

Can negative numbers be prime?

No, by definition prime numbers are positive. We only consider positive integers greater than 1 when talking about primes.

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