Question

1. which statement is true?

a the only factors of 3 are 3 and 1; therefore, 3 is prime.
b the only factors of 4 are 4 and 1; therefore, 4 is prime.
c the only factors of 5 are 5 and 1; therefore, 5 is composite.
d the only factors of 8 are 8 and 1; therefore, 8 is composite.

Explanation:

Step1: Analyze Option A

Factors of 3 are 1 and 3 (since \(1\times3 = 3\)). A prime number has exactly two distinct positive divisors: 1 and itself. So 3 is prime. But the statement says "the only factors of 3 are 3 and 1; therefore, 3 is prime"—wait, but let's check other options too. Wait, no, let's re - check. Wait, the first part: factors of 3 are 1 and 3, that's correct. And 3 is prime (since it has exactly two distinct positive factors). But wait, let's check other options.

Step2: Analyze Option B

Factors of 4: \(1\times4 = 4\), \(2\times2 = 4\). So factors of 4 are 1, 2, 4. So the statement "the only factors of 4 are 4 and 1" is wrong. Also, 4 is composite (not prime), so this option is incorrect.

Step3: Analyze Option C

Factors of 5: \(1\times5 = 5\). So factors of 5 are 1 and 5. A prime number has exactly two distinct positive factors, so 5 is prime, not composite. So this option is incorrect.

Step4: Analyze Option D

Factors of 8: \(1\times8 = 8\), \(2\times4 = 8\). So factors of 8 are 1, 2, 4, 8. The statement "the only factors of 8 are 8 and 1" is wrong. Also, 8 is composite, but the reason given is wrong.

Wait, going back to Option A: The factors of 3 are 1 and 3 (exactly two distinct positive factors), so 3 is prime. The statement in Option A says "The only factors of 3 are 3 and 1; therefore, 3 is prime"—this is correct because a prime number is defined as a positive integer greater than 1 that has exactly two distinct positive divisors: 1 and itself.

Answer:

A. The only factors of 3 are 3 and 1; therefore, 3 is prime.