Number Classification Challenge: Is 14 Prime or Composite?

Prime Classification with Even Numbers

Is the number equal to n n prime or composite?

n=14 n=14

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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, therefore it is composite
00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is the number equal to n n prime or composite?

n=14 n=14

2

Step-by-step solution

To solve this problem, we'll determine if the number n=14 n = 14 is prime or composite by checking its divisibility by numbers other than 1 and 14 itself.

  • Step 1: Recognize that a prime number has only two distinct divisors: 1 and itself.
  • Step 2: A composite number has additional divisors.
  • Step 3: Start checking for divisibility from the smallest primes: 2, 3, 5, etc.

Now, let's work through these steps:

Step 1: Given n=14 n = 14 , check divisibility:
Since 14 is an even number, it is divisible by 2 (i.e., 14÷2=7 14 \div 2 = 7 ).

Step 2: As 2 is a divisor other than 1 and itself, 14 cannot be a prime number.

Step 3: Verify divisibility confirms that 14 is composed of factors 2×7 2 \times 7 .

Therefore, the solution to the problem is that the number 14 is composite.

3

Final Answer

Composite

Key Points to Remember

Essential concepts to master this topic
  • Definition: Prime numbers have exactly two divisors: 1 and themselves
  • Technique: Check divisibility by 2 first: 14÷2=7 14 \div 2 = 7
  • Verify: Find all factors of 14: 1, 2, 7, 14 (more than 2 factors) ✓

Common Mistakes

Avoid these frequent errors
  • Assuming larger numbers are automatically prime
    Don't think that 14 is prime just because it's bigger than single digits = wrong classification! Many students forget that even numbers (except 2) always have 2 as a factor. Always check divisibility by small primes like 2, 3, 5 first.

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 can't 14 be prime if it's not that small?

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Size doesn't determine if a number is prime! The key is how many factors it has. Since 14 is even, it's automatically divisible by 2, giving it at least 3 factors: 1, 2, and 14.

Is 2 the only even prime number?

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Yes! 2 is the only even prime because all other even numbers are divisible by 2, giving them more than two factors. This makes them composite by definition.

How do I quickly check if a number is composite?

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Start with the smallest primes: 2, 3, 5, 7, 11... If any of these divide your number evenly (with no remainder), it's composite! For 14: 14÷2=7 14 \div 2 = 7 with no remainder.

What's the difference between factors and divisors?

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They're the same thing! Both terms mean numbers that divide evenly into your original number. For 14, the factors (or divisors) are: 1, 2, 7, and 14.

Do I need to check all numbers up to 14?

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No! You only need to check up to the square root of your number. For 14, that's about 3.7, so checking 2 and 3 is enough to determine if it's composite.

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