Which term describes a factor that is also a prime number?

The term that describes a factor that is also a prime number is "prime factor." A prime factor is defined as a factor that is a prime number — that is, it has exactly two distinct positive divisors: 1 and itself. Prime numbers include numbers like 2, 3, 5, 7, 11, and so forth, which cannot be formed by multiplying two smaller natural numbers.

Understanding the context of prime factors is essential in mathematics, especially in topics such as factorization and finding the greatest common divisor (GCD). Recognizing that prime factors serve as building blocks for all integers is crucial, as every integer greater than 1 can be uniquely expressed as a product of prime factors, according to the fundamental theorem of arithmetic.

In contrast, a composite factor would be one that can be divided evenly by numbers other than 1 and itself, which means it has more than two distinct positive divisors. An integer factor encompasses any factor of a number, without the restriction of being prime, while a common factor refers to any number that can divide two or more numbers without a remainder, which can include both prime and composite numbers. These distinctions are key in understanding the properties of numbers and their relationships in mathematics.