Question
Is the number 14 a prime number? Explain why or why not.
Ask by Higgins Gordon. in South Africa
Jan 04,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
14 is not a prime number because it has divisors other than 1 and itself (specifically, 2 and 7).
Solution
No, the number 14 is not a prime number.
Understanding Prime Numbers
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors:
- 1
- The number itself
In other words, a prime number cannot be formed by multiplying two smaller natural numbers.
Analyzing the Number 14
Let’s examine the divisors of 14:
- 1 × 14 = 14
- 2 × 7 = 14
From the above, we can see that 14 has the following positive divisors:
- 1
- 2
- 7
- 14
Since 14 has more than two divisors (1, 2, 7, and 14), it does not meet the criteria of having exactly two distinct positive divisors.
Conclusion
Because 14 can be divided evenly by 1, 2, 7, and 14, it has more than two factors. Therefore, 14 is classified as a composite number, not a prime number.
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Simplify this solution Bonus Knowledge
The number 14 is not a prime number because it has more divisors than just 1 and itself. Specifically, 14 can be divided evenly by 1, 2, 7, and 14. Because it has divisors other than 1 and 14, it qualifies as a composite number instead of a prime.
In ancient times, numbers were often categorized into prime and composite, with primes being the “building blocks” of all numbers. The Romans, for example, used primes in various architectural and engineering feats. Understanding which numbers are prime helps in everything from cryptography to computer algorithms today!
