Is 7 Prime or Composite? Number Classification Challenge

Q: Why isn't 1 considered prime?

By definition, a prime number must have exactly two divisors. The number 1 only has one divisor (itself), so it's neither prime nor composite - it's a special case!

Q: Do I need to check all numbers less than 7?

No! You only need to check divisors up to $ \sqrt{7} \approx 2.6 $. This means checking just the number 2. If larger factors existed, smaller ones would too!

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

Prime: Exactly 2 divisors (1 and itself)Composite: More than 2 divisorsExample: 6 is composite because it has divisors 1, 2, 3, and 6.

Q: Are there any patterns to help identify primes?

For small numbers, memorize the first few primes: 2, 3, 5, 7, 11, 13... Notice that except for 2, all primes are odd (but not all odd numbers are prime!).

Q: How do I check if 7 divided by 2 gives a whole number?

Calculate: $ 7 \div 2 = 3.5 $. Since this has a decimal part (.5), it's not a whole number, so 2 doesn't divide evenly into 7.

Prime Number Classification with Small Integers

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

$n=7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the number prime or composite?

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

00:06 Therefore, if the number is divisible by another factor, it is not prime

00:12 The number has no other factors, meaning it is prime

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?

$n=7$

Step-by-step solution

To determine whether the number $n = 7$ is prime or composite, we follow these steps:

Step 1: Acknowledge the definition of prime numbers. A prime number is any number greater than 1 that has no divisors other than 1 and itself.
Step 2: We begin by checking if the number $7$ is greater than 1. Since $7 > 1$ , it is eligible to be considered a prime number.
Step 3: We examine whether $7$ has any divisors other than 1 and itself.
Step 4: For a number to be composite, it must have additional divisors apart from 1 and itself. Let's check the possible divisors.
Step 5: Since 7 is a small number, its divisors would be smaller than $\sqrt{7} \approx 2.64$ . The only whole number less than or equal to 2 not including 1 is 2.
Step 6: We check divisibility: 7 divided by 2 is not a whole number, confirming 7 is not divisible by any number other than 1 and itself.

Therefore, we conclude that the number $n = 7$ is indeed a Prime number.

Final Answer

Prime

Key Points to Remember

Essential concepts to master this topic

Definition: Prime numbers have exactly two divisors: 1 and themselves
Technique: Check divisibility by numbers up to $\sqrt{7} \approx 2.6$
Check: 7 ÷ 2 = 3.5 (not whole), so 7 is prime ✓

Common Mistakes

Avoid these frequent errors

Confusing prime definition with odd/even
Don't think all odd numbers are prime = wrong classification! Not all odd numbers are prime (like 9 = 3 × 3). Always check if the number has exactly two divisors: 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

Why isn't 1 considered prime?

By definition, a prime number must have exactly two divisors. The number 1 only has one divisor (itself), so it's neither prime nor composite - it's a special case!

Do I need to check all numbers less than 7?

No! You only need to check divisors up to $\sqrt{7} \approx 2.6$ . This means checking just the number 2. If larger factors existed, smaller ones would too!

What's the difference between prime and composite?

Prime: Exactly 2 divisors (1 and itself)
Composite: More than 2 divisors
Example: 6 is composite because it has divisors 1, 2, 3, and 6.

Are there any patterns to help identify primes?

For small numbers, memorize the first few primes: 2, 3, 5, 7, 11, 13... Notice that except for 2, all primes are odd (but not all odd numbers are prime!).

How do I check if 7 divided by 2 gives a whole number?

Calculate: $7 \div 2 = 3.5$ . Since this has a decimal part (.5), it's not a whole number, so 2 doesn't divide evenly into 7.

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