Identify Common Factors, Common Multiples and Prime Numbers 2 - Reasoning

The topic of identifying common factors, common multiples, and prime numbers is an essential part of mathematical reasoning and number theory. Common factors are numbers that divide exactly into two or more numbers without leaving a remainder. For instance, when looking at the numbers 12 and 18, common factors would include 1, 2, 3, and 6. These are the numbers that can divide both 12 and 18 evenly. Understanding common factors is crucial for simplifying fractions and solving problems involving ratios and proportions.

Common multiples, on the other hand, are numbers that are multiples of two or more numbers. For example, the first few common multiples of 3 and 4 would be 12, 24, and 36, as these numbers are multiples of both 3 and 4. Recognising common multiples is particularly useful when finding the least common multiple (LCM) for adding and subtracting fractions with different denominators. Prime numbers are numbers greater than 1 that only have two factors: 1 and the number itself. Examples of prime numbers are 2, 3, 5, 7, and 11. Identifying prime numbers is fundamental for various aspects of mathematics, including prime factorisation and understanding the building blocks of all numbers.