Find the Missing Digit in the Composite Number: _3

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

A prime number has exactly 2 factors: 1 and itself. A composite number has more than 2 factors. For example, 13 is prime (factors: 1, 13) but 63 is composite (factors: 1, 3, 7, 9, 21, 63).

Q: Why isn't 1 considered prime or composite?

The number 1 is neither prime nor composite by definition. It only has one factor (itself), so it doesn't fit either category. Prime and composite numbers must be greater than 1.

Q: Can I use divisibility rules to help?

Yes! For example, if a number ends in 3, check if the sum of digits is divisible by 3. For $ 63 $: 6 + 3 = 9, and 9 ÷ 3 = 3, so 63 is divisible by 3.

Composite Numbers with Two-Digit Identification

Fill in the blanks for a composite number:

$\square3$

❤️ 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:

$\square3$

Step-by-step solution

To solve this problem, we must identify a digit to place in front of 3, creating a two-digit composite number:

Step 1: Evaluate $13$ . This number is only divisible by 1 and 13, making it a prime number.
Step 2: Evaluate $23$ . This number is only divisible by 1 and 23, making it a prime number.
Step 3: Evaluate $33$ . The number 33 can be divided by 1, 3, 11, and 33. Since it has divisors other than 1 and itself, $33$ is a composite number.
Step 4: Evaluate $43$ . This number is only divisible by 1 and 43, making it a prime number.

After evaluating, we find that placing the digit 6 in front of 3 results in the number 63, which is divisible by 1, 3, 7, 9, 21, and 63 and is therefore a composite number. But since the answer claims that 6 results in a composite, let's review the choice 63 and see how 3 results in the same.

Finally, the solution is: Digit is 6, resulting in composite number 63.

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Definition: Composite numbers have more than two factors (divisors)
Technique: Test each digit: 63 = 3 × 21, has multiple factors
Check: Count factors of your answer: 1, 3, 7, 9, 21, 63 ✓

Common Mistakes

Avoid these frequent errors

Confusing prime and composite definitions
Don't think composite means 'only divisible by 1 and itself' = that's prime! Composite numbers have MORE than two factors, not fewer. Always remember: composite = multiple factors, prime = exactly two factors.

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?

A prime number has exactly 2 factors: 1 and itself. A composite number has more than 2 factors. For example, 13 is prime (factors: 1, 13) but 63 is composite (factors: 1, 3, 7, 9, 21, 63).

How do I quickly find all factors of a number?

Start with 1 and the number itself. Then test small numbers: does 2 divide evenly? 3? 4? Keep going until you reach the square root. Remember: if a divides the number, then the quotient is also a factor!

Why isn't 1 considered prime or composite?

The number 1 is neither prime nor composite by definition. It only has one factor (itself), so it doesn't fit either category. Prime and composite numbers must be greater than 1.

Can I use divisibility rules to help?

Yes! For example, if a number ends in 3, check if the sum of digits is divisible by 3. For $63$ : 6 + 3 = 9, and 9 ÷ 3 = 3, so 63 is divisible by 3.

What if multiple digits work in the blank?

Test each option systematically! In this problem, you need to check $13, 23, 33, 43, 53, 63, 73, 83, 93$ and identify which ones are composite. Don't assume there's only one answer!

🌟 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