Prime Time Class 6 Notes: CBSE Maths Chapter 5

Common factors: Common factors are numbers that divide two or more numbers without leaving a remainder. In other words, they are the numbers that are shared between the factors of each number you are comparing.

How to Find Common Factors:

• List the Factors: First, find all the factors of each number. For example, factors of 12 are 1, 2, 3, 4, 6, and 12; factors of 18 are 1, 2, 3, 6, 9, and 18.

• Identify the Common Ones: Look at the lists and pick out the numbers that appear in both lists. For 12 and 18, the common factors are 1, 2, 3, and 6.

Perfect Number

A perfect number is a special type of number that is equal to the sum of its proper divisors, excluding itself.

What are Proper Divisors?

Proper divisors are numbers that divide the given number evenly (without leaving a remainder) but do not include the number itself.

Example: 6 is a perfect number. Its proper divisors are 1, 2, and 3. If you add these divisors together (1 + 2 + 3), the sum is 6, which is the number itself.

Prime Numbers:

• Definition: Numbers greater than 1 with exactly two factors: 1 and themselves.

• Examples: 2, 3, 5, 7, 11, 13, 17, 19.

• Note: 2 is the only even prime number; all other prime numbers are odd.

Composite Numbers:

• Definition: Numbers greater than 1 that have more than two factors.

• Examples: 4, 6, 8, 9, 10, 12, 15.

• Note: Composite numbers can be divided evenly by numbers other than 1 and themselves.

Co-prime Numbers for Safekeeping Treasures

Co-prime numbers (also called relatively prime numbers) are two or more numbers that have no common factors other than 1. In other words, the only number that divides both of them exactly is 1.

Co-prime numbers are useful in various mathematical problems and real-life applications. They are often used in problems involving fractions, ratios, and simplifying mathematical expressions. Understanding co-prime numbers helps in solving problems related to dividing objects or sharing resources.

Prime Factorization:

• Definition: Expressing a number as a product of its prime factors.

• Example: For 30, the prime factorization is 2 × 3 × 5.

• Method: Use factor trees or repeated division by prime numbers.

Sieve of Eratosthenes:

• Purpose: To find all prime numbers up to a certain number.

• How it Works: Cross out multiples of each prime number starting from 2. The numbers that remain are primes.

Greatest Common Divisor (GCD):

• Definition: The largest number that divides two or more numbers without leaving a remainder.

• Finding GCD: Use prime factorization to determine common factors and multiply them.

• Example: GCD of 12 and 18 is 6 (common factors are 2 × 3).

Least Common Multiple (LCM):

• Definition: The smallest number that is a multiple of two or more numbers.

• Finding LCM: Use prime factorization to find the highest power of each prime in the numbers and multiply them.

• Example: LCM of 4 and 5 is 20.

5 Important Topics of Class 6 Maths Chapter 5 Prime Time

Importance of Maths Class 6 Chapter 5 Prime Time Notes

• Revision notes help us quickly understand and remember key concepts before exams.

• They save time by focusing on essential information and skipping unnecessary details.

• These notes simplify complex topics, making them easier to understand and use.

• They provide practical examples that show how theoretical knowledge is used in real-life situations.

• Revision notes ensure thorough preparation by covering all important topics in a structured manner.

• They increase confidence by clearly understanding what to expect in exams.

• Accessible formats like PDFs allow for easy studying anytime and anywhere.

Tips for Learning the Class 6 Maths Chapter 5 Prime Time Notes

• Start by clearly understanding what prime and composite numbers are. Remember, prime numbers have only two factors (1 and itself), while composite numbers have more.

• Work on identifying prime and composite numbers by practising with different sets of numbers. Make a list to help visualise the patterns.

• Familiarise yourself with this method for finding all prime numbers up to a certain number. It’s a useful technique for quickly listing primes.

• Use factor trees to decompose numbers into their prime factors. This method will make prime factorization easier to understand and perform.

Conclusion

In Class 6 Maths Chapter 5 Prime Time by vedantu explored the prime and composite numbers. We learned that prime numbers are those with only two factors and themselves, while composite numbers have more. Understanding prime factorization helps break down numbers into their building blocks, making complex problems simpler. We've also practised using methods like the Sieve of Eratosthenes to find prime numbers efficiently. With these concepts, you'll be better equipped to solve problems related to GCD and LCM. Keep practising identifying prime numbers and using these techniques to strengthen your grasp of the topic. These foundational skills will be valuable for more advanced mathematical concepts in the future.

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