Prime Number Identification: Which Number Meets Prime Criteria?

Q: Why isn't 6 a prime number?

6 has more than two factors! You can divide 6 by 1, 2, 3, and 6. Since $ 6 ÷ 2 = 3 $ and $ 6 ÷ 3 = 2 $, it's composite, not prime.

Q: How do I test if 11 is really prime?

Try dividing 11 by all numbers from 2 up to $ \sqrt{11} ≈ 3.3 $. Test: $ 11 ÷ 2 = 5.5 $, $ 11 ÷ 3 = 3.67 $. Since neither gives a whole number, 11 is prime!

Q: What makes 4 and 10 not prime?

$ 4 = 2 × 2 $ and $ 10 = 2 × 5 $. Both numbers have multiple factor pairs beyond 1 and themselves, making them composite numbers.

Q: Is there a quick way to spot non-prime numbers?

Yes! Even numbers (except 2) are never prime because they're divisible by 2. Numbers ending in 0 or 5 (except 5) divide by 5. This eliminates 4, 6, and 10 quickly!

Q: Do I need to memorize all prime numbers?

Not all of them! But knowing the first few primes helps: 2, 3, 5, 7, 11, 13, 17, 19, 23. You can always test divisibility when you're unsure.

Prime Identification with Divisibility Testing

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

00:04 A prime number is only divisible by itself and 1

00:08 Therefore, if the number is divisible by another factor, it is not prime

00:23 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

Test for divisibility:

$6$ : It is divisible by $2$ and $3$ , so it is not a prime number.
$11$ : It is only divisible by $1$ and $11$ , making it a prime number.
$10$ : It is divisible by $2$ and $5$ , so it is not a prime number.
$4$ : It is divisible by $2$ , so it is not a prime number.

Based on the steps above, the number that is a prime number is $11$ .

Final Answer

$11$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime numbers have exactly two factors: 1 and themselves
Testing: Check if 11 divides by 2, 3, 5, 7, 10
Verification: Confirm 11 ÷ 2 = 5.5, 11 ÷ 3 = 3.67 (not whole) ✓

Common Mistakes

Avoid these frequent errors

Thinking 1 is a prime number
Don't count 1 as prime = wrong classification! One only has one factor (itself), but primes need exactly two different factors. Always remember primes start at 2.

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

Why isn't 6 a prime number?

6 has more than two factors! You can divide 6 by 1, 2, 3, and 6. Since $6 ÷ 2 = 3$ and $6 ÷ 3 = 2$ , it's composite, not prime.

How do I test if 11 is really prime?

Try dividing 11 by all numbers from 2 up to $\sqrt{11} ≈ 3.3$ . Test: $11 ÷ 2 = 5.5$ , $11 ÷ 3 = 3.67$ . Since neither gives a whole number, 11 is prime!

What makes 4 and 10 not prime?

$4 = 2 × 2$ and $10 = 2 × 5$ . Both numbers have multiple factor pairs beyond 1 and themselves, making them composite numbers.

Is there a quick way to spot non-prime numbers?

Yes! Even numbers (except 2) are never prime because they're divisible by 2. Numbers ending in 0 or 5 (except 5) divide by 5. This eliminates 4, 6, and 10 quickly!

Do I need to memorize all prime numbers?

Not all of them! But knowing the first few primes helps: 2, 3, 5, 7, 11, 13, 17, 19, 23. You can always test divisibility when you're unsure.

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