Number Classification: Is 22 Prime or Composite?

Q: Why do I only need to check up to the square root of 22?

Because factors come in pairs! If 22 has a factor larger than $ \sqrt{22} \approx 4.7 $, then it must also have a corresponding factor smaller than 4.7. Since we check all numbers up to 4.7, we'll find both factors.

Q: How do I know if a number is prime or composite?

Prime: Has exactly 2 factors (1 and itself). Composite: Has more than 2 factors. If you find even one factor other than 1 and the number itself, it's composite!

Q: What about the number 1 - is it prime or composite?

Neither! The number 1 is special - it only has one factor (itself), so it doesn't fit the definition of prime (which needs exactly 2 factors) or composite (which needs more than 2 factors).

Prime Classification with Divisibility Testing

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

$n=22$

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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

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

00:11 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?

$n=22$

Step-by-step solution

To solve this problem, we'll determine whether $n = 22$ is a prime or composite number.

We follow these steps:

Step 1: List possible divisors of $22$ other than $1$ and $22$ itself.
Step 2: Test $22$ for divisibility by these numbers.
Step 3: Conclude based on the results.

Step 1: The numbers to consider are $2, 3, 4, 5, ...$ up to the square root of $22$ , rounded up, which is approximately 4.7. Thus, feasible numbers are $2, 3, 4$ .

Step 2: Check each number:

$\text{Is } 22 \div 2$ a whole number? Yes, $22 \div 2 = 11$ .

Step 3: Since $22$ is divisible by $2$ , it has at least one divisor other than $1$ and itself.

Therefore, $n = 22$ is a composite number.

Thus, the correct choice from the given options is: Composite.

Final Answer

Composite

Key Points to Remember

Essential concepts to master this topic

Definition: Prime has exactly two factors: 1 and itself
Technique: Test divisibility by primes up to $\sqrt{22} \approx 4.7$ : check 2, 3
Check: Since $22 ÷ 2 = 11$ with no remainder, 22 is composite ✓

Common Mistakes

Avoid these frequent errors

Testing all numbers up to 22 instead of just up to the square root
Don't check every number from 2 to 21 for divisibility = wasted time and confusion! You only need to check up to the square root because factors come in pairs. Always test divisibility only up to $\sqrt{n}$ to save time and avoid errors.

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 do I only need to check up to the square root of 22?

Because factors come in pairs! If 22 has a factor larger than $\sqrt{22} \approx 4.7$ , then it must also have a corresponding factor smaller than 4.7. Since we check all numbers up to 4.7, we'll find both factors.

What if a number is even like 22?

Great observation! Any even number greater than 2 is automatically composite because it's divisible by 2. So 22 is composite since $22 ÷ 2 = 11$ .

How do I know if a number is prime or composite?

Prime: Has exactly 2 factors (1 and itself). Composite: Has more than 2 factors. If you find even one factor other than 1 and the number itself, it's composite!

What about the number 1 - is it prime or composite?

Neither! The number 1 is special - it only has one factor (itself), so it doesn't fit the definition of prime (which needs exactly 2 factors) or composite (which needs more than 2 factors).

Do I need to check if 22 is divisible by 4?

Not necessary! Since we already found that 22 is divisible by 2, we know it's composite. But if you want to be thorough: $22 ÷ 4 = 5.5$ , so 4 doesn't divide 22 evenly.

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