Graduate Management Admission Test (GMAT) Practice Test

What is the prime factor of a prime number?

1. Itself

2. The number 1

3. The sum of its digits

4. It has no prime factors

The correct answer is: Itself

The correct response to the question about the prime factor of a prime number is that it is itself. To understand why this is the case, consider the definition of a prime number: a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that when you are identifying prime factors, the only two numbers that can divide a prime number evenly are 1 and the prime number itself. Since the question specifically focuses on prime factors, and since only the number itself meets the criteria of being a prime factor (as it is greater than 1 and only divisible by itself), it confirms that the prime factor of a prime is indeed the prime number itself. The choice regarding the number 1 is not accurate in this context because while 1 is a divisor of every integer, it is not considered a prime number and does not qualify as a prime factor. The option about the sum of its digits doesn't relate to prime factors either, as prime factorization refers specifically to the prime numbers that multiply to give a particular integer. Lastly, the idea that a prime number has no prime factors is incorrect, as a prime number itself is precisely its own prime factor.