Number Classification: Is n=4 Prime or Composite?

Q: Why isn't 1 considered a prime number?

By definition, a prime number must have exactly two divisors. The number 1 only has one divisor (itself), so it doesn't qualify as prime. It's neither prime nor composite - it's in a special category!

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

Prime: Exactly 2 divisors (1 and itself)Composite: More than 2 divisorsExamples: 7 is prime (divisors: 1, 7), but 6 is composite (divisors: 1, 2, 3, 6)

Q: Is 2 the only even prime number?

Yes! Since all other even numbers are divisible by 2, they automatically have at least three divisors (1, 2, and themselves), making them composite. Only 2 has exactly two divisors: 1 and 2.

Q: How can I remember which small numbers are prime?

For numbers 1-10: 2, 3, 5, 7 are the only primes. Remember the phrase '2, 3, 5, 7 - primes from 1 to heaven!' All others (4, 6, 8, 9, 10) are composite.

Prime Number Identification with Small Integers

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

$n=4$

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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?

00:03 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

00:11 The number has other factors, meaning it is composite

00:17 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?

$n=4$

Step-by-step solution

To determine if the number $n = 4$ is prime or composite, we will follow these steps:

Step 1: Understand the definitions.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number has additional divisors.
Step 2: Identify divisors of 4.
We list out the divisors of 4, starting from 1: They are 1, 2, and 4.
Step 3: Analyze the divisors.
The number 4 has more than two divisors: 1, 2, and 4. This means it can be divided by numbers other than 1 and itself.

Conclusion: Since 4 has divisors other than 1 and itself (specifically, it is divisible by 2), it is not a prime number. Therefore, 4 is classified as a composite number.

Therefore, the solution to the problem is Composite.

Final Answer

Composite

Key Points to Remember

Essential concepts to master this topic

Definition: Prime numbers have exactly two divisors: 1 and itself
Method: List all divisors of 4: 1, 2, 4 (three divisors)
Check: Since 4 has more than two divisors, it's composite ✓

Common Mistakes

Avoid these frequent errors

Confusing prime definition with 'can only be divided by 1'
Don't say a number is prime just because it's divisible by 1 = every number divides by 1! This ignores the key requirement of having exactly two divisors. Always check that a prime has only 1 and itself as divisors, no others.

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 1 considered a prime number?

By definition, a prime number must have exactly two divisors. The number 1 only has one divisor (itself), so it doesn't qualify as prime. It's neither prime nor composite - it's in a special category!

How do I quickly find all divisors of a small number?

Start with 1 and work your way up! For any number n, check if 1, 2, 3, 4... divide evenly into n. Stop when you reach n itself. List all numbers that divide evenly.

What's the difference between prime and composite again?

Prime: Exactly 2 divisors (1 and itself)
Composite: More than 2 divisors
Examples: 7 is prime (divisors: 1, 7), but 6 is composite (divisors: 1, 2, 3, 6)

Is 2 the only even prime number?

Yes! Since all other even numbers are divisible by 2, they automatically have at least three divisors (1, 2, and themselves), making them composite. Only 2 has exactly two divisors: 1 and 2.

How can I remember which small numbers are prime?

For numbers 1-10: 2, 3, 5, 7 are the only primes. Remember the phrase '2, 3, 5, 7 - primes from 1 to heaven!' All others (4, 6, 8, 9, 10) are composite.

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