In number theory, a prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Conversely, a composite number has additional divisors beyond 1 and itself. This distinction is crucial in determining whether 15 is a prime number.
Factors of 15
To ascertain the classification of 15, we examine its factors:
- 1: 15 ÷ 1 = 15
- 3: 15 ÷ 3 = 5
- 5: 15 ÷ 5 = 3
- 15: 15 ÷ 15 = 1
These calculations reveal that 15 has four positive divisors: 1, 3, 5, and 15. Since it has more than two distinct positive divisors, 15 is classified as a composite number.
Prime Factorization of 15
Prime factorization involves expressing a composite number as a product of its prime factors. For 15, this process is as follows:
- Divide by the smallest prime number (2): 15 is odd and not divisible by 2.
- Proceed to the next prime number (3): 15 ÷ 3 = 5.
- Since 5 is a prime number, the factorization concludes here.
Therefore, the prime factorization of 15 is:
15 = 3 × 5
This confirms that 15 is the product of the prime numbers 3 and 5.
Understanding Composite Numbers
A composite number is a positive integer that has at least one positive divisor other than 1 and itself. In the case of 15, the additional divisors are 3 and 5, confirming its composite status. Recognizing the factors of a number is essential in distinguishing between prime and composite numbers.
FAQ
- Is 15 a prime number?
- No, 15 is not a prime number; it has divisors other than 1 and itself, specifically 3 and 5.
- What are the factors of 15?
- The factors of 15 are 1, 3, 5, and 15.
- What is the prime factorization of 15?
- The prime factorization of 15 is 3 × 5.
- Why is 15 considered a composite number?
- 15 is considered a composite number because it has more than two distinct positive divisors.
- How can you determine if a number is prime or composite?
- To determine if a number is prime, check if it has exactly two distinct positive divisors: 1 and itself. If it has more, it is composite.
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- To determine if a number is prime, check if it has exactly two distinct positive divisors: 1 and itself. If it has more, it is composite.