Fill in the Blanks: Identify a Composite Number Challenge

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

Prime numbers have exactly 2 divisors (1 and themselves), like 2, 3, 5, 7. Composite numbers have more than 2 divisors, like 4, 6, 8, 9.

Q: Is 1 prime or composite?

Actually, 1 is neither prime nor composite! It only has one divisor (itself), so it doesn't fit either definition. It's a special case.

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

Yes! Even numbers greater than 2 are always composite (divisible by 1, 2, and themselves). Also, numbers ending in 5 (except 5) are composite because they're divisible by 5.

Q: Why isn't 2 composite if it's even?

Great question! Even though 2 is even, it only has exactly 2 divisors (1 and 2). Remember: composite means more than 2 divisors, not exactly 2.

Prime and Composite Number Identification

Fill in the blanks for a composite number:

$\square1$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the blanks for a composite number:

$\square1$

Step-by-step solution

To solve this problem, we need to identify which of the given numbers is a composite number by analyzing the options provided:

Option 1: $6$ — The divisors of 6 are 1, 2, 3, and 6. Since it has more than two distinct divisors, it is a composite number.
Option 2: $2$ — The divisors of 2 are 1 and 2. It has only two distinct divisors, so it is a prime number.
Option 3: $7$ — The divisors of 7 are 1 and 7. It has only two distinct divisors, so it is a prime number.
Option 4: $3$ — The divisors of 3 are 1 and 3. It has only two distinct divisors, so it is a prime number.

Based on the list above, we conclude that the number $6$ is a composite number because it has more than two distinct divisors.

Therefore, the correct choice for the composite number is $6$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Definition: Composite numbers have more than two distinct divisors
Method: List all divisors - 6 has divisors 1, 2, 3, 6
Verify: Count divisors: more than 2 means composite ✓

Common Mistakes

Avoid these frequent errors

Confusing prime and composite definitions
Don't think that having exactly two divisors makes a number composite = backwards thinking! This actually defines prime numbers. Always remember: composite numbers have MORE than two divisors, while prime numbers have exactly two.

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

What's the difference between prime and composite numbers?

Prime numbers have exactly 2 divisors (1 and themselves), like 2, 3, 5, 7. Composite numbers have more than 2 divisors, like 4, 6, 8, 9.

Is 1 prime or composite?

Actually, 1 is neither prime nor composite! It only has one divisor (itself), so it doesn't fit either definition. It's a special case.

How do I find all the divisors of a number?

Start with 1 and the number itself. Then check each number in between: does it divide evenly? For 6: try 2 (yes, 6÷2=3) and 3 (yes, 6÷3=2). So divisors are 1, 2, 3, 6.

Are there any patterns to help identify composite numbers?

Yes! Even numbers greater than 2 are always composite (divisible by 1, 2, and themselves). Also, numbers ending in 5 (except 5) are composite because they're divisible by 5.

Why isn't 2 composite if it's even?

Great question! Even though 2 is even, it only has exactly 2 divisors (1 and 2). Remember: composite means more than 2 divisors, not exactly 2.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime