What does an expression indicating that "a" is divisible by 3 suggest?

What does an expression indicating that "a" is divisible by 3 suggest?

• A. The value of "a" is always a prime number
• B. "a" can be expressed as 3k, where k is an integer
• C. "a" must be an even number
• D. "a" is an irrational number

Answer: (B)

The expression indicating that "a" is divisible by 3 means that there exists an integer k such that "a" can be expressed in the form of 3k. This representation shows that "a" can be written as some multiple of 3, which confirms its divisibility. This is a fundamental concept in number theory that aligns perfectly with the definition of divisibility. The other options do not align with the fundamental property of divisibility by 3. For example, a prime number is defined as a natural number greater than 1 with no positive divisors other than 1 and itself, and while some prime numbers are divisible by 3, such as 3 itself, many are not, making that assumption incorrect. Similarly, being an even number is not a requirement for a number to be divisible by 3; for instance, 9 is divisible by 3 and is odd. Lastly, the nature of "a" being irrational is unrelated to divisibility, as divisibility typically applies to integers. Therefore, the best interpretation of "a" being divisible by 3 is through the expression 3k, where k is an integer, which highlights the essence of divisibility in arithmetic.

The expression indicating that "a" is divisible by 3 means that there exists an integer k such that "a" can be expressed in the form of 3k. This representation shows that "a" can be written as some multiple of 3, which confirms its divisibility. This is a fundamental concept in number theory that aligns perfectly with the definition of divisibility.

The other options do not align with the fundamental property of divisibility by 3. For example, a prime number is defined as a natural number greater than 1 with no positive divisors other than 1 and itself, and while some prime numbers are divisible by 3, such as 3 itself, many are not, making that assumption incorrect. Similarly, being an even number is not a requirement for a number to be divisible by 3; for instance, 9 is divisible by 3 and is odd. Lastly, the nature of "a" being irrational is unrelated to divisibility, as divisibility typically applies to integers. Therefore, the best interpretation of "a" being divisible by 3 is through the expression 3k, where k is an integer, which highlights the essence of divisibility in arithmetic.