Define a prime factor.

A prime factor is a factor of a number that is a prime number itself.

Prime factors are the building blocks of numbers. To understand them better, let's break down the concept. A factor of a number is any whole number that can be multiplied by another whole number to get the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because these numbers can be multiplied in pairs to make 12 (e.g., 2 × 6 = 12).

A prime number, on the other hand, is a number greater than 1 that has no positive divisors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11. When we talk about prime factors, we are specifically referring to those factors of a number that are prime.

To find the prime factors of a number, you can use a method called prime factorisation. This involves dividing the number by the smallest prime number (which is 2) and continuing the process with the quotient until you end up with 1. For instance, to find the prime factors of 60, you would start by dividing by 2 (the smallest prime number):
60 ÷ 2 = 30,
30 ÷ 2 = 15,
15 ÷ 3 = 5,
5 ÷ 5 = 1.

So, the prime factors of 60 are 2, 2, 3, and 5. This can also be written as \(2^2 \times 3 \times 5\). Understanding prime factors is essential in various areas of mathematics, including simplifying fractions, finding the greatest common divisor (GCD), and solving problems involving ratios and proportions.