Composite Number Identification: Select the Non-Prime Integer

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

Prime numbers have exactly 2 factors: 1 and themselves (like 2, 3, 5, 7). Composite numbers have more than 2 factors because they can be divided by other numbers too!

Q: Why is 9 composite but 7 is prime?

Because $ 9 ÷ 3 = 3 $ with no remainder! This means 9 has factors: 1, 3, and 9. But 7 only divides evenly by 1 and 7, so it's prime.

Q: Is 1 prime or composite?

Actually, 1 is neither prime nor composite! It's a special case because it only has one factor (itself). Prime and composite numbers must have at least two factors.

Q: Can even numbers be prime?

Only one even number is prime: 2! All other even numbers are composite because they're divisible by 2. So 4, 6, 8, 10... are all composite.

Q: What if I can't remember which numbers are prime?

Don't memorize - test them! Try dividing by 2, 3, 5, 7... If you find any divisor other than 1 and the number itself, it's composite. Practice makes it faster!

Prime and Composite Classification with Single-Digit Numbers

Choose the composite 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 composite number from the options.

Step-by-step solution

To solve this problem, we will follow these detailed steps:

Step 1: Understand the definitions: A composite number has more than two divisors. A prime number has exactly two divisors.
Step 2: Examine each choice to determine its type:

$9$ : Check divisibility by numbers other than 1 and itself. $9$ is divisible by 3, as $9 \div 3 = 3$ . Thus, 9 is composite.
$7$ : Check divisibility. Only divides evenly by 1 and 7. Thus, 7 is prime.
$3$ : Check divisibility. Only divides evenly by 1 and 3. Thus, 3 is prime.
$5$ : Check divisibility. Only divides evenly by 1 and 5. Thus, 5 is prime.

Step 3: Conclude which number is composite based on the divisor check:

Since 9 is the only number with more than two divisors (1, 3, and 9), it is the composite number.

Therefore, the solution to the problem is $9$ .

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Definition: Composite numbers have more than two factors (divisors)
Method: Test divisibility: $9 ÷ 3 = 3$ shows 9 is composite
Check: List all factors: 9 has factors 1, 3, 9 (more than two) ✓

Common Mistakes

Avoid these frequent errors

Confusing prime and composite definitions
Don't think composite means "made of primes" or that larger numbers are always composite = wrong classification! Students mix up the definitions. Always remember: composite numbers have MORE than two factors, while prime numbers have EXACTLY two factors (1 and themselves).

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

What's the difference between prime and composite numbers?

Prime numbers have exactly 2 factors: 1 and themselves (like 2, 3, 5, 7). Composite numbers have more than 2 factors because they can be divided by other numbers too!

Why is 9 composite but 7 is prime?

Because $9 ÷ 3 = 3$ with no remainder! This means 9 has factors: 1, 3, and 9. But 7 only divides evenly by 1 and 7, so it's prime.

Is 1 prime or composite?

Actually, 1 is neither prime nor composite! It's a special case because it only has one factor (itself). Prime and composite numbers must have at least two factors.

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

Try dividing by small primes: 2, 3, 5. If any division gives a whole number, it's composite! For example:

$9 ÷ 3 = 3$ → composite
$7 ÷ 2, 7 ÷ 3$ → both have remainders → prime

Can even numbers be prime?

Only one even number is prime: 2! All other even numbers are composite because they're divisible by 2. So 4, 6, 8, 10... are all composite.

What if I can't remember which numbers are prime?

Don't memorize - test them! Try dividing by 2, 3, 5, 7... If you find any divisor other than 1 and the number itself, it's composite. Practice makes it faster!

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