Determine if 36 is Prime or Composite: Number Classification Problem

Q: Why do I only need to test divisors up to the square root?

Because divisors come in pairs! For 36, if you find 2 × 18 = 36, you've found both divisors at once. Once you test up to $ \sqrt{36} = 6 $, you've checked all possible pairs.

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

Prime numbers have exactly 2 factors: 1 and themselves (like 2, 3, 5, 7). Composite numbers have more than 2 factors (like 4, 6, 8, 9). The number 1 is neither prime nor composite.

Q: Is there a quick way to tell if 36 is composite?

Yes! Since 36 is even (ends in an even digit), it's automatically divisible by 2. Any even number greater than 2 must be composite because it has 2 as a factor.

Q: What are all the factors of 36?

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. Since it has more than just 1 and 36 as factors, it's definitely composite!

Q: Can a number be both prime and composite?

No! Every whole number greater than 1 is either prime or composite, never both. It's like being either tall or short - you can't be both at the same time.

Prime Classification with Divisibility Testing

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

$n=36$

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Step-by-step video solution

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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, 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?

$n=36$

Step-by-step solution

To determine whether 36 is a prime or composite number, we need to check if it has divisors other than 1 and 36:

Step 1: Calculate the square root of 36, which is 6. This means we only need to test divisibility by numbers up to and including 6.
Step 2: Check divisibility by 2. Since 36 is an even number (divisible by 2), it has a divisor other than 1 and itself.

Therefore, since 36 is divisible by 2 (and also by other numbers such as 3, 4, and more), it has divisors other than just 1 and 36. This means it cannot be a prime number.

Conclusively, the number 36 is Composite.

Final Answer

Composite

Key Points to Remember

Essential concepts to master this topic

Definition: Prime has exactly two factors: 1 and itself only
Method: Test divisors up to √36 = 6, starting with 2
Check: If any divisor works, the number is composite ✓

Common Mistakes

Avoid these frequent errors

Only testing if a number divides evenly by 2
Don't stop after finding 36 ÷ 2 = 18 and call it composite! This misses the complete understanding of what makes numbers composite. Always recognize that finding ANY divisor other than 1 and the number itself proves it's composite, and 36 has many divisors: 2, 3, 4, 6, 9, 12, 18.

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 do I only need to test divisors up to the square root?

Because divisors come in pairs! For 36, if you find 2 × 18 = 36, you've found both divisors at once. Once you test up to $\sqrt{36} = 6$ , you've checked all possible pairs.

What's the difference between prime and composite numbers?

Prime numbers have exactly 2 factors: 1 and themselves (like 2, 3, 5, 7). Composite numbers have more than 2 factors (like 4, 6, 8, 9). The number 1 is neither prime nor composite.

Is there a quick way to tell if 36 is composite?

Yes! Since 36 is even (ends in an even digit), it's automatically divisible by 2. Any even number greater than 2 must be composite because it has 2 as a factor.

What are all the factors of 36?

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. Since it has more than just 1 and 36 as factors, it's definitely composite!

Can a number be both prime and composite?

No! Every whole number greater than 1 is either prime or composite, never both. It's like being either tall or short - you can't be both at the same time.

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