Prime Number Identification: Which Number Fits the Definition?

Q: Is 1 considered a prime number?

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

Q: Why isn't 9 a prime number?

Even though 9 is odd, it has more than two factors: 1, 3, and 9. Since $ 9 = 3 \times 3 $, it can be divided evenly by 3, making it a composite number, not prime.

Q: What's the difference between prime and composite numbers?

Prime numbers have exactly 2 factors (1 and themselves), while composite numbers have 3 or more factors. For example: 7 is prime (factors: 1, 7) but 12 is composite (factors: 1, 2, 3, 4, 6, 12).

Q: Are there any patterns to help me remember prime numbers?

Yes! Except for 2, all prime numbers are odd (but not all odd numbers are prime). The first few primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23... Notice how they can't be divided by any smaller primes.

Prime Number Recognition with Multiple Choice Options

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

00:08 Therefore, let's check if the number is divisible by another, non-prime factor:

00:22 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 determine which of the given numbers is a prime number, we need to check each number for divisibility:

For $9$ : It is divisible by $3$ (since $9 \div 3 = 3$ ), so it is not a prime number.
For $10$ : It is divisible by $2$ (since $10 \div 2 = 5$ ), so it is not a prime number.
For $7$ : It is only divisible by $1$ and $7$ (itself). It cannot be divided by any other numbers except 1 and itself without leaving a remainder, so $7$ is a prime number.
For $12$ : It is divisible by $2$ (since $12 \div 2 = 6$ ), so it is not a prime number.

Thus, the only number in the list that satisfies the condition of being prime, having exactly two distinct positive divisors, is $7$ .

Therefore, the solution to the problem is $7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Definition: A prime number has exactly two factors: 1 and itself
Technique: Check divisibility by small primes like 2, 3, 5, 7
Verification: Confirm no other factors exist besides 1 and the number itself ✓

Common Mistakes

Avoid these frequent errors

Confusing prime with odd numbers
Don't assume all odd numbers are prime = wrong identification! Numbers like 9 and 15 are odd but composite (9 = 3×3, 15 = 3×5). Always check for factors other than 1 and the number itself.

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, a prime number must have exactly two distinct factors: 1 and itself. Since 1 only has one factor (itself), it doesn't qualify as prime.

How do I quickly check if a number like 7 is prime?

For small numbers, check if they're divisible by primes smaller than the number. For 7: it's not divisible by 2 (it's odd), not by 3 (7÷3 = 2 remainder 1), and not by 5. Since we've checked all primes less than 7, 7 is prime!

Why isn't 9 a prime number?

Even though 9 is odd, it has more than two factors: 1, 3, and 9. Since $9 = 3 \times 3$ , it can be divided evenly by 3, making it a composite number, not prime.

What's the difference between prime and composite numbers?

Prime numbers have exactly 2 factors (1 and themselves), while composite numbers have 3 or more factors. For example: 7 is prime (factors: 1, 7) but 12 is composite (factors: 1, 2, 3, 4, 6, 12).

Are there any patterns to help me remember prime numbers?

Yes! Except for 2, all prime numbers are odd (but not all odd numbers are prime). The first few primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23... Notice how they can't be divided by any smaller primes.

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