Maths Notes Class 6 Chapter 5 Prime Time Ganita Prakash

Idli-Sambar game

The Idli-Sambar game is a fun and educational game that helps children learn about multiples of numbers, particularly focusing on 3 and 5. The rules are:

1. Players sit in a circle and take turns counting aloud.
2. When a number is a multiple of 3 (e.g., 3, 6, 9, etc.), the player says “Idli” instead of the number.
3. When a number is a multiple of 5 (e.g., 5, 10, 15, etc.), the player says “Sambar” instead of the number.
4. If a number is a multiple of both 3 and 5 (e.g., 15, 30, 45, etc.), the player says “Idli-Sambar.”
5. Players who make a mistake are out of the game, and the game continues until only one player remains.

Purpose:

The game helps students practice and identify multiples of 3 and 5 while keeping them engaged in a fun and interactive manner.

Prime Numbers:

• A prime number has only two factors: 1 and itself.
• Examples of prime numbers: 2, 3, 5, 7, 11, 13, etc.
• 2 is the only even prime number.

Composite Numbers:

• A composite number has more than two factors.
• Examples of composite numbers: 4, 6, 8, 9, 12, etc.
• The number 1 is neither prime nor composite.

Factors and Multiples:

• A factor of a number divides it exactly without leaving a remainder.
• A multiple of a number is obtained by multiplying the number by an integer.
• Example: Factors of 12 are 1, 2, 3, 4, 6, and 12. Multiples of 3 are 3, 6, 9, 12, 15, etc.

Common Factors and Common Multiples:

• Common factors of two numbers are factors shared by both numbers.
• Common multiples are numbers that are multiples of both numbers.
• Example: Common factors of 12 and 18 are 1, 2, 3, and 6. Common multiples are 36, 72, etc.

Prime Factorization:

• Prime factorization is expressing a number as a product of prime numbers.
• Example: Prime factorization of 56 is
• 56=2×2×2×7.

Co-prime Numbers:

• Two numbers are co-prime if their only common factor is 1.
• Example: 4 and 9 are co-prime because their only common factor is 1.

Divisibility Rules:

1. Divisibility by 2:
   • A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
2. Divisibility by 3:
   A number is divisible by 3 if the sum of its digits is divisible by 3.
   • Example: 123 is divisible by 3 because 1+2+3=61 + 2 + 3 = 6 1+2+3=6, which is divisible by 3.
3. Divisibility by 5:
   • A number is divisible by 5 if its last digit is 0 or 5.
4. Divisibility by 10:
   • A number is divisible by 10 if its last digit is 0.
5. Divisibility by 4 and 8:
   • A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
   • A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Important Terms:

• Sieve of Eratosthenes: A method to find all prime numbers up to a certain number.
• Perfect Numbers: A number is perfect if the sum of its factors (excluding itself) equals the number.
  • Example: 6 is a perfect number because the sum of its divisors (1, 2, 3) is 6.