Class 6 Notes - Playing with Numbers

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Playing with Numbers

This chapter explores the fascinating world of numbers and their properties. Students will learn about factors, multiples, prime and composite numbers, divisibility rules, and how to solve puzzles and problems using these concepts.

1. Factors and Multiples

  • Factor: A number that divides another number exactly.
  • Multiple: The result of multiplying a number by an integer.
  • Example: 3 is a factor of 12; 12 is a multiple of 3.

2. Prime and Composite Numbers

  • Prime Number: Has exactly two factors: 1 and itself (e.g., 2, 3, 5, 7, 11).
  • Composite Number: Has more than two factors (e.g., 4, 6, 8, 9, 10).
  • 1 is neither prime nor composite.

3. Tests of Divisibility

  • Divisibility by 2: Number ends in 0, 2, 4, 6, 8.
  • Divisibility by 3: Sum of digits is divisible by 3.
  • Divisibility by 5: Number ends in 0 or 5.
  • Divisibility by 10: Number ends in 0.
  • Other rules for 4, 6, 8, 9, 11, etc.

4. Common Factors and Common Multiples

  • Common Factor: A number that is a factor of two or more numbers.
  • Common Multiple: A number that is a multiple of two or more numbers.
  • Highest Common Factor (HCF): The greatest common factor.
  • Lowest Common Multiple (LCM): The smallest common multiple.

5. Perfect Numbers and Co-prime Numbers

  • Perfect Number: A number whose sum of all its factors (except itself) equals the number (e.g., 6, 28).
  • Co-prime Numbers: Two numbers having only 1 as their common factor (e.g., 4 and 9).

6. Prime Factorization

  • Expressing a number as a product of its prime factors.
  • Example: 12 = 2 × 2 × 3

7. Puzzles and Patterns

  • Number puzzles using factors, multiples, and divisibility.
  • Finding missing numbers in patterns.

8. Word Problems

  1. Find all factors of 24.
  2. Is 37 a prime number?
  3. What is the LCM of 6 and 8?
  4. Are 8 and 15 co-prime?
  5. Express 60 as a product of its prime factors.

9. Practice Exercises

  1. List all multiples of 7 less than 50.
  2. Find the HCF of 18 and 24.
  3. Which numbers between 1 and 20 are prime?
  4. Write the divisibility rule for 9.
  5. Find the common factors of 12 and 16.

10. Summary

  • Understanding factors, multiples, and divisibility helps solve many mathematical problems.
  • Prime and composite numbers are building blocks of numbers.
  • HCF and LCM are useful in real-life situations.
  • Playing with numbers develops logical thinking and problem-solving skills.