Is 20 a Prime or Composite Number? Number Theory Classification

Q: Is 2 the only even prime number?

Yes! The number 2 is the only even prime because all other even numbers are divisible by 2, giving them at least three factors: 1, 2, and themselves.

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

Try dividing by small prime numbers (2, 3, 5, 7, 11...) up to the square root of your number. If none divide evenly, it's prime!

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

Prime numbers have exactly 2 factors (1 and themselves). Composite numbers have 3 or more factors. The number 1 is neither prime nor composite.

Q: Why isn't 1 considered prime?

By definition, prime numbers must have exactly two different factors. Since 1 only has one factor (itself), it doesn't meet the prime criteria.

Prime Classification with Factor Analysis

Is the number equal to $n$ prime or composite?

$n=20$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the number composite or prime?

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

00:12 The number has other factors, therefore it is composite

00:15 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

Is the number equal to $n$ prime or composite?

$n=20$

Step-by-step solution

To determine if $n = 20$ is prime or composite, we need to examine its divisors.

Step 1: Identify divisors of 20, other than 1 and 20 itself.
Since 20 is an even number, it is divisible by 2. So, 2 is a divisor of 20.
Step 2: Check divisibility by other small numbers:
- 20 divided by 4 equals 5 (another divisor).
- Additionally, $20 \div 5 = 4$ , confirming 5 is also a divisor.

Since 20 has divisors other than 1 and itself (including 2, 4, and 5), it is not a prime number.

Therefore, the number $n = 20$ is Composite.

Final Answer

Composite

Key Points to Remember

Essential concepts to master this topic

Definition: Prime has exactly two divisors: 1 and itself only
Technique: Check divisibility by small primes like $20 ÷ 2 = 10$
Verification: List all factors: 1, 2, 4, 5, 10, 20 shows composite ✓

Common Mistakes

Avoid these frequent errors

Confusing prime definition with odd numbers
Don't think all odd numbers are prime and all even numbers are composite = wrong classification! While most even numbers (except 2) are composite, some odd numbers like 9, 15, 21 are also composite. Always check for factors other than 1 and the number itself.

Practice Quiz

Test your knowledge with interactive questions

Is the number equal to $$ n $$ prime or composite?

$$ n=29 $$

FAQ

Everything you need to know about this question

Is 2 the only even prime number?

Yes! The number 2 is the only even prime because all other even numbers are divisible by 2, giving them at least three factors: 1, 2, and themselves.

How do I quickly check if a number is prime?

Try dividing by small prime numbers (2, 3, 5, 7, 11...) up to the square root of your number. If none divide evenly, it's prime!

What's the difference between prime and composite?

Prime numbers have exactly 2 factors (1 and themselves). Composite numbers have 3 or more factors. The number 1 is neither prime nor composite.

Why isn't 1 considered prime?

By definition, prime numbers must have exactly two different factors. Since 1 only has one factor (itself), it doesn't meet the prime criteria.

Can I use a calculator to find all factors?

Yes! Divide your number by integers starting from 2. If you get a whole number result, you've found a factor pair. For 20: $20 ÷ 4 = 5$ shows 4 and 5 are factors.

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