NCERT Class 6 Maths Chapter 5
Prime Time
This chapter explores the fascinating world of prime numbers with Class 6 CBSE students, covering concepts like prime and composite numbers, prime factorization, LCM, and HCF. Students use tools like factor trees and divisibility rules to break numbers into their prime factors. Understanding prime numbers provides the number theory foundation for fractions, algebra, and cryptography in higher mathematics.
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Key Terms
- Prime Number
- A natural number greater than 1 that has exactly two factors: 1 and itself (e.g., 2, 3, 5, 7, 11, 13).
- Composite Number
- A natural number greater than 1 that has more than two factors; i.e., it can be divided by numbers other than 1 and itself (e.g., 4, 6, 8, 9).
- Prime Factorization
- Expressing a composite number as a product of its prime factors (e.g., 36 = 2 × 2 × 3 × 3).
- HCF (Highest Common Factor)
- The largest factor common to two or more numbers; also called the Greatest Common Divisor (GCD).
- LCM (Lowest Common Multiple)
- The smallest multiple common to two or more numbers; used for adding or subtracting fractions with unlike denominators.
- Factor Tree
- A diagram used to break down a number into its prime factors step by step, branching like a tree.
Frequently Asked Questions
What is a prime number in Class 6 Maths?▾
A prime number is a number greater than 1 that has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17. Note: 2 is the only even prime number. 1 is neither prime nor composite.
What is the difference between prime and composite numbers in Class 6?▾
A prime number has exactly two factors (1 and itself), like 7. A composite number has more than two factors, like 12 (factors: 1, 2, 3, 4, 6, 12). The number 1 is neither prime nor composite.
How do you find the HCF and LCM of two numbers in Class 6?▾
For HCF: find all common factors and pick the largest. For LCM: find the prime factorization of both numbers and multiply each prime factor at its highest power. Example: HCF(12,18)=6; LCM(12,18)=36.
What is prime factorization in Class 6 Maths Chapter 5?▾
Prime factorization is writing a number as a product of only prime numbers. For example, 60 = 2 × 2 × 3 × 5 or 2² × 3 × 5. A factor tree helps by repeatedly dividing by the smallest prime factor until all factors are prime.
What is the Sieve of Eratosthenes in Class 6 Maths?▾
The Sieve of Eratosthenes is an ancient method to find all prime numbers up to a given number. Start with a number grid, keep 2 and cross out all multiples of 2, keep 3 and cross out all multiples of 3, and so on. Numbers remaining are primes.
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