Identify the Prime Number Among the List: A Basic Number Theory Challenge

Q: Is 1 considered a prime number?

No, 1 is not prime! By definition, a prime number must have exactly two divisors. Since 1 only has one divisor (itself), it doesn't qualify as prime.

Q: How do I quickly test if a number is prime?

Start by checking divisibility by small primes: 2, 3, 5, 7, 11. If none divide evenly and your number is less than 121, it's prime! For larger numbers, test up to the square root.

Q: Why isn't 27 prime if it's odd?

Being odd doesn't make a number prime! $ 27 = 3 \times 9 $, so it has divisors 1, 3, 9, and 27. Since it has more than two divisors, it's composite, not prime.

Q: Can even numbers be prime?

Only one even number is prime: 2. All other even numbers are divisible by 2, giving them at least three divisors (1, 2, and themselves), so they're composite.

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

Prime: Exactly 2 divisors (1 and itself)Composite: More than 2 divisorsNeither: The number 1 (special case)

Prime Numbers 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

00:03 A prime number is only divisible by itself and 1

00:07 Therefore, if the number is divisible by another factor, it is not prime

00:41 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Which of the numbers is a prime number?

Step-by-step solution

Let's determine which of the given numbers is a prime number. A prime number is a natural number greater than 1 that is only divisible by 1 and itself.

We have the following numbers to consider: $22, 23, 20,$ and $27$ .

22: This number is divisible by 1, 2, 11, and 22. Therefore, it is not a prime number since it has divisors other than 1 and itself.
23: This number is only divisible by 1 and 23. It satisfies the definition of a prime number, as it has no divisors other than 1 and 23.
20: This number is divisible by 1, 2, 4, 5, 10, and 20. It has divisors other than 1 and itself, making it not a prime number.
27: This number is divisible by 1, 3, 9, and 27. Like the others, it is not a prime number because it has divisors other than 1 and itself.

Thus, after evaluating all options, we find that only $23$ is a prime number.

Therefore, the solution to the problem is $23$ .

Final Answer

$23$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime has exactly two divisors: one and itself
Testing: Check divisibility by small primes like $2, 3, 5, 7$
Verification: Confirm 23 ÷ 2, 23 ÷ 3, 23 ÷ 5 all leave remainders ✓

Common Mistakes

Avoid these frequent errors

Confusing odd numbers with prime numbers
Don't assume all odd numbers are prime = wrong classification! Numbers like 9, 15, 21, 27 are odd but composite (have more than two divisors). Always check for divisors beyond 1 and the number 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

Is 1 considered a prime number?

No, 1 is not prime! By definition, a prime number must have exactly two divisors. Since 1 only has one divisor (itself), it doesn't qualify as prime.

How do I quickly test if a number is prime?

Start by checking divisibility by small primes: 2, 3, 5, 7, 11. If none divide evenly and your number is less than 121, it's prime! For larger numbers, test up to the square root.

Why isn't 27 prime if it's odd?

Being odd doesn't make a number prime! $27 = 3 \times 9$ , so it has divisors 1, 3, 9, and 27. Since it has more than two divisors, it's composite, not prime.

Can even numbers be prime?

Only one even number is prime: 2. All other even numbers are divisible by 2, giving them at least three divisors (1, 2, and themselves), so they're composite.

What's the difference between prime and composite numbers?

Prime: Exactly 2 divisors (1 and itself)
Composite: More than 2 divisors
Neither: The number 1 (special case)

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Identify the Prime Number Among the List: A Basic Number Theory Challenge

Prime Numbers with Divisibility Testing

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Is 1 considered a prime number?

How do I quickly test if a number is prime?

Why isn't 27 prime if it's odd?

Can even numbers be prime?

What's the difference between prime and composite numbers?

🌟 Unlock Your Math Potential

More Questions

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