Explore Composite Numbers: Fill in the Blanks with 3

Q: How do I quickly tell if a number is composite?

Look for obvious factors first! If a number ends in 0, 2, 4, 6, or 8, it's divisible by 2. If digits sum to a multiple of 3, it's divisible by 3. For $ 33 $: 3+3=6, which is divisible by 3!

Q: Why isn't 13 composite if it has the digit 3?

The digits in a number don't determine if it's composite - the factors do! $ 13 $ only has factors 1 and 13, making it prime, not composite.

Q: How do I find all factors of 33?

Test division systematically: $ 33 ÷ 1 = 33 $, $ 33 ÷ 3 = 11 $, $ 33 ÷ 11 = 3 $, $ 33 ÷ 33 = 1 $. So the factors are 1, 3, 11, and 33.

Q: Could the answer be a different digit?

Let's check! $ 13 $, $ 23 $, and $ 43 $ are all prime numbers. Only $ 33 $ is composite, so 3 is the only correct answer.

Composite Numbers with Two-Digit Format

Fill in the blanks for a composite number:

$\square3$

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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 need to determine which number of the form $\square3$ is composite. A composite number has more than two distinct positive divisors.

Step 1: Possible numbers from the format $\square3$ are 13, 23, 33, and 43.
Step 2: Check divisibility and identify which numbers are not prime:
$13$ : Prime number as its only divisors are 1 and 13.
$23$ : Prime number as its only divisors are 1 and 23.
$33$ : Composite, divisible by 1, 3, 11, and 33.
$43$ : Prime number as its only divisors are 1 and 43.

Step 3: From the analysis, 33 is a composite number.

Therefore, filling the blank with the digit 3 gives the composite number $33$ .

Thus, the solution to the problem is to fill the blank with $3$ to form a composite number.

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Definition: Composite numbers have more than two positive divisors
Method: Test each possibility: 13, 23, 33, 43 for divisibility
Verification: Count all divisors of 33: 1, 3, 11, 33 = four divisors ✓

Common Mistakes

Avoid these frequent errors

Confusing prime and composite definitions
Don't think composite means 'made of two digits' = wrong classification! Composite refers to having multiple factors, not digit count. Always check if a number has divisors other than 1 and itself.

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

How do I quickly tell if a number is composite?

Look for obvious factors first! If a number ends in 0, 2, 4, 6, or 8, it's divisible by 2. If digits sum to a multiple of 3, it's divisible by 3. For $33$ : 3+3=6, which is divisible by 3!

Why isn't 13 composite if it has the digit 3?

The digits in a number don't determine if it's composite - the factors do! $13$ only has factors 1 and 13, making it prime, not composite.

What's the smallest composite number?

The smallest composite number is 4 because it has factors 1, 2, and 4. Remember: 1 is neither prime nor composite!

How do I find all factors of 33?

Test division systematically: $33 ÷ 1 = 33$ , $33 ÷ 3 = 11$ , $33 ÷ 11 = 3$ , $33 ÷ 33 = 1$ . So the factors are 1, 3, 11, and 33.

Could the answer be a different digit?

Let's check! $13$ , $23$ , and $43$ are all prime numbers. Only $33$ is composite, so 3 is the only correct answer.

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