1. The user has listed 21 topics related to Chapter 1: Prime numbers, HCF, LCM. 2. These topics cover index notation, prime factorization, square roots, cube roots, HCF, LCM, and their applications. 3. Since no specific problem is asked, I will provide a brief explanation of the key concepts: **Prime Factorization:** Every number can be expressed as a product of prime numbers raised to powers, e.g., $$360 = 2^3 \times 3^2 \times 5^1$$. **HCF (Highest Common Factor):** The greatest number that divides two or more numbers exactly. It is found by taking the minimum powers of common prime factors. **LCM (Lowest Common Multiple):** The smallest number divisible by two or more numbers. It is found by taking the maximum powers of all prime factors involved. **Relationship:** For two numbers $a$ and $b$, $$HCF(a,b) \times LCM(a,b) = a \times b$$. **Square Root and Cube Root by Prime Factorization:** - To find the square root, pair the prime factors and take one from each pair. - To find the cube root, group prime factors in triples and take one from each triple. These concepts are foundational for solving problems involving divisibility, simplification, and number properties.