Which of the following statements about prime and composite numbers is correct?
2019
Which of the following statements about prime and composite numbers is correct?
Answer: B. A composite number can be odd. — ConceptA prime number is a natural number greater than 1 with exactly two positive factors: 1 and itself. A composite number is a natural number greater than…
- A.
The sum of two prime numbers is always a prime number.
- B.
A composite number can be odd.
- C.
The smallest prime number is 1.
- D.
There is no even prime number.
Attempted by 49 students.
Show answer & explanation
Correct answer: B
Concept
A prime number is a natural number greater than 1 with exactly two positive factors: 1 and itself.
A composite number is a natural number greater than 1 that has more than two positive factors. A universal statement is disproved by one counterexample.
Application
Consider 9. Its positive factors are 1, 3, and 9, so it has more than two factors and is composite. Since 9 is odd, an odd composite number exists.
Contrast
“The sum of two prime numbers is always prime” fails for 3 + 5 = 8, and 8 has factors other than 1 and 8.
“The smallest prime number is 1” fails because 1 has only one positive factor, whereas a prime requires exactly two.
“There is no even prime number” fails because 2 is even and its only positive factors are 1 and 2.
Therefore, the correct statement is: A composite number can be odd.