In this lesson, we will explore the concepts of factorization, prime factors, and highest common factors (HCF) using real-life and mathematical examples. We will also learn how to find the least common multiple (LCM) and apply these concepts to practical problems.
Factorization: We will start by understanding how to factorize numbers into their prime components. For example, to factorize 120, we break it down into its prime factors.
Finding Factors: You will learn how to find all the factors of a number and list those below a certain limit. For instance, list five factors of 520 that are less than 100.
Multiples: We will identify multiples of a given number, such as listing five multiples of 28.
Arrangement Problems: We will solve problems involving the arrangement of objects (like chairs) in rows, ensuring that each row has an equal number of items. For example, determine the number of ways to arrange 180 chairs with a specific number of chairs per row.
Prime Factors: Learn to find the prime factors of various numbers and express numbers as products of these prime factors.
Highest Common Factor (HCF): Understand how to find the HCF of pairs of numbers by listing their factors and using their prime factorizations. For example, determine the HCF of 36 and 48.
Packing and Distribution: Apply the concept of HCF to practical scenarios like packing fruits into bags so that each bag has an equal number of fruits and no fruit is left over.
Least Common Multiple (LCM): Find the LCM of triples of numbers to determine the smallest number that is a multiple of all given numbers.
Practical Application: Solve problems involving intervals, such as finding out when multiple events occur together again, using LCM.
By mastering these concepts, you’ll be able to solve various mathematical problems and understand how these principles apply to everyday situations.
