Experts have designed these Class 7 Maths Notes and Part 2 Chapter 3 Finding Common Ground Class 7 Notes for effective learning.
Class 7 Maths Chapter 3 Finding Common Ground Notes
Class 7 Finding Common Ground Notes
→ In the previous class, we explored concepts such as common multiples, common factors, prime and composite numbers, and prime factorisation. We also learned how to find the highest common factor (HCF) and the least common multiple (LCM) using various methods.
These topics laid the groundwork for more advanced applications. In this class, we will build on that knowledge by diving deeper into efficient techniques for prime factorisation, determining the HCF and LCM, and uncovering the fascinating relationship between them.
→ Prime Factorisation is the process of expressing a number as a product of its prime factors.
→ The Highest Common Factor (HCF) is the largest factor that is common to a group of numbers.
- To find the HCF, we begin by identifying the largest common sub-part in the prime factorisation of the numbers.
- We can determine the HCF by examining the minimum number of occurrences of each prime factor in the prime factorisations of numbers.
→ The Least Common Multiple (LCM) is the smallest among all the common multiples of a group of numbers.
- Every common multiple must include the prime factorisation of the numbers involved.
- To determine the LCM, we examine the prime factors present in the prime factorisations. For each prime factor, we take the highest number of times it appears across all the factorisations to construct the LCM.
→ A statement describing a pattern or a property that holds true in all the possible cases is called a general statement. This process is called generalisation.
→ HCF × LCM = Product of the numbers.