Prime Number Identification: Analyzing Integer Properties

Q: Is 1 considered a prime number?

No, 1 is not prime! By definition, prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it doesn't qualify as prime.

Q: Why isn't 4 a prime number if it's small?

Size doesn't determine if a number is prime! $ 4 = 2 \times 2 $, so 4 has factors 1, 2, and 4. Since it has more than two factors, it's composite, not prime.

Q: What makes 5 special compared to the other numbers?

$ 5 $ is only divisible by 1 and 5 itself. Unlike 4 (divisible by 2), 8 (divisible by 2 and 4), or 12 (divisible by 2, 3, 4, and 6), 5 has no other factors.

Q: Are there any patterns to help identify prime numbers?

All primes except 2 are odd numbersPrimes greater than 3 end in 1, 3, 7, or 9But remember: not all numbers following these patterns are prime!

Prime Numbers with Divisibility Testing

Which of the numbers is a prime number?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the prime numbers

00:03 A prime number is only divisible by itself and 1

00:07 Therefore, we'll check if the number is divisible by another factor, not prime:

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the numbers is a prime number?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given numbers: $8$ , $4$ , $5$ , $12$ .
Step 2: Verify the primality of each number.

Now, let's work through each step:
Step 1: The numbers provided are $8$ , $4$ , $5$ , $12$ .
Step 2: We need to determine if each number is a prime by checking if they have divisors other than 1 and themselves:

$8$ is divisible by $2$ , so it has divisors besides 1 and 8. Therefore, 8 is not a prime number.
$4$ is divisible by $2$ , so it has divisors besides 1 and 4. Therefore, 4 is not a prime number.
$5$ is not divisible by any integer other than 1 and 5. Thus, 5 is a prime number.
$12$ is divisible by $2$ and $3$ , so it has divisors besides 1 and 12. Therefore, 12 is not a prime number.

Therefore, the solution to the problem is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime numbers have exactly two factors: 1 and themselves
Technique: Test divisibility by small primes like 2, 3, 5
Check: Verify 5 has no divisors between 2 and 4 ✓

Common Mistakes

Avoid these frequent errors

Confusing even numbers with prime numbers
Don't think that larger numbers like 8 or 12 could be prime = automatic wrong answer! All even numbers except 2 are composite because they're divisible by 2. Always check if a number is divisible by 2 first.

Practice Quiz

Test your knowledge with interactive questions

Is the number equal to $$ n $$ prime or composite?

$$ n=10 $$

FAQ

Everything you need to know about this question

Is 1 considered a prime number?

No, 1 is not prime! By definition, prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it doesn't qualify as prime.

Why isn't 4 a prime number if it's small?

Size doesn't determine if a number is prime! $4 = 2 \times 2$ , so 4 has factors 1, 2, and 4. Since it has more than two factors, it's composite, not prime.

How do I quickly check if a number is prime?

Test divisibility by small primes: 2, 3, 5, 7, etc. If the number divides evenly by any of these, it's not prime. You only need to test up to the square root of the number!

What makes 5 special compared to the other numbers?

$5$ is only divisible by 1 and 5 itself. Unlike 4 (divisible by 2), 8 (divisible by 2 and 4), or 12 (divisible by 2, 3, 4, and 6), 5 has no other factors.

Are there any patterns to help identify prime numbers?

All primes except 2 are odd numbers
Primes greater than 3 end in 1, 3, 7, or 9
But remember: not all numbers following these patterns are prime!

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