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CBSE Notes Class 6 Maths Chapter 5 Prime Time
Chapter 5: Prime Time in CBSE Class 6 Maths introduces students to the fascinating world of prime numbers, common factors, common multiples, and divisibility rules. It explores key concepts like prime factorisation, co-prime numbers, and divisibility tests, helping students understand the relationships between numbers and simplifying mathematical problems through these fundamental concepts.
1.0Common Factors
Factors are the numbers that can divide a given number completely. For example, the factors of 6 are 1, 2, 3, and 6 because these are the numbers that divide 6 without a remainder.
When we compare two or more numbers, the common factors are the numbers that divide both numbers completely.
Example: Common factors of 12 and 18 :
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- The factors of 18 are 1, 2, 3, 6, 9, and 18.
So, the common factors of 12 and 18 are 1, 2, 3, and 6. These are the numbers that can divide both 12 and 18 without leaving a remainder.
2.0Common Multiples
A multiple is the result of multiplying a number by any whole number. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.
Common multiples are the multiples that are shared by two or more numbers.
Example: Common Multiple of 4 and 6 :
- The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on.
- The multiples of 6 are 6, 12, 18, 24, 30, and so on.
So, the common multiples of 4 and 6 are 12, 24, 36, and so on.
Note: The smallest common multiple of two numbers is called the Least Common Multiple or LCM.
3.0Prime Numbers
A Prime Number is a number greater than 1 that has only two factors: 1 and the number itself. In other words, a prime number can only be divided by 1 and itself without leaving a remainder.
Here is a list of all prime numbers from 1 to 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
4.0Co-prime Numbers
Two numbers are co-prime if their Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) is 1. In other words, co-prime numbers don’t share any factors other than 1.
Example: 5 and 9, 8 and 15, 9 and 28, 5 and 14, 12 and 25, 7 and 30, etc
5.0Prime Factorisation
Prime Factorisation is the process of breaking down a number into a product of its prime factors.
Examples:
- Prime Factorisation of 12 is 2 × 2 × 3.
- Prime Factorisation of 18 is 2 × 3 × 3.
6.0Divisibility Tests
- A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- A number is divisible by 5 if its last digit is 0 or 5.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- A number is divisible by 10 if its last digit is 0.
7.0Benefits of CBSE Notes for Class 6 Maths Chapter 5 - Prime Time
- Mastering Prime Factorisation: You will learn how to break down any composite number into a product of its prime factors using methods like factor trees or division. This skill is crucial for finding the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM).
- Understanding Divisibility Tests: The CBSE Notes for Class 6 provides easy ways to check if a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 without performing actual division. This saves time and reduces errors. For instance, you'll learn that a number is divisible by 3 if the sum of its digits is divisible by 3 (e.g., for 123, 1+2+3=6, which is divisible by 3, so 123 is also divisible by 3).
- Preparation for Advanced Topics: The concepts learned in this chapter form a strong foundation for more advanced topics in mathematics that you will encounter in higher classes.
- Quick Revision: CBSE Notes provide a concise summary of the chapter, making it easy to revise the key concepts and formulas before tests or exams.
- Improved Problem-Solving Skills: A clear understanding of the concepts and techniques discussed in the notes will enhance your ability to solve a variety of problems related to factors, multiples, and prime numbers.