Class 6 Mathematics Chapter 3 Number Play

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I. Chapter Summary:

Chapter 3, Number Play, introduces students to various interesting patterns and properties related to numbers. It explores concepts such as divisibility, factors and multiples, prime and composite numbers, and patterns formed by these numbers. The chapter helps build number sense and prepares students for advanced topics in arithmetic and number theory. It encourages students to recognize and extend number patterns, understand divisibility rules, and apply them to solve mathematical problems.

II. Key Concepts Covered:

• Divisibility Rules: Guidelines to determine if a number is divisible by 2, 3, 4, 5, 6, 9, and 10 without performing actual division.

• Factors and Multiples: Understanding factors of a number, common factors, multiples, and common multiples.

• Prime Numbers: Numbers having exactly two factors: 1 and the number itself.

• Composite Numbers: Numbers having more than two factors.

• Patterns in Numbers: Recognizing repeating and growing sequences in factors and multiples.

• Finding Prime Factors: Using factor trees to break down composite numbers into prime factors.

• Special Number Properties: Like numbers divisible by 9 have digit sums divisible by 9.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. Which of the following is a prime number?
   a) 15
   b) 13
   c) 21
   d) 27
   Answer: b) 13
   (PYQ 2021)

2. A number is divisible by 3 if:
   a) The last digit is 0
   b) Sum of digits is divisible by 3
   c) The number ends with 5
   d) It is even
   Answer: b) Sum of digits is divisible by 3
   (PYQ 2020)

3. What is the smallest composite number?
   a) 1
   b) 2
   c) 4
   d) 3
   Answer: c) 4

4. Which of the following is NOT a factor of 12?
   a) 3
   b) 4
   c) 5
   d) 6
   Answer: c) 5

(B) Short Answer Questions (2/3 Marks):

1. Define prime and composite numbers with examples.

2. Explain the divisibility rule for 5.

3. Find the factors of 24.

4. What is a factor tree? Draw a factor tree for 18.

(C) Long Answer Questions (5 Marks):

1. List the prime factors of 48 using a factor tree.

2. Explain the rule of divisibility for 9 with an example.

3. Find the common factors and common multiples of 6 and 8.

4. Write a detailed note on the difference between prime and composite numbers.

(D) HOTS (Higher Order Thinking Skills) Questions:

1. If a number is divisible by both 2 and 3, is it always divisible by 6? Justify.

2. Using divisibility rules, find the smallest number divisible by 2, 3, and 5.

IV. Key Formulas/Concepts:

• Divisibility Rules:

  • By 2: Last digit is even

  • By 3: Sum of digits divisible by 3

  • By 5: Last digit 0 or 5

  • By 9: Sum of digits divisible by 9

• Prime Factorization: Breaking a composite number into its prime factors.

• Common Factors and Multiples: Factors/multiples common to two or more numbers.

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs):

• 2022: MCQ on prime numbers (1 mark)

• 2021: Short answer on divisibility rules (2 marks)

• 2020: Long answer on prime factorization (5 marks)

• 2019: HOTS on common multiples (3 marks)

VIII. Real-World Application Examples:

• Cryptography: Prime numbers used in encoding messages.

• Inventory Management: Factors and multiples help in packaging and arranging items.

• Scheduling: Multiples used to determine cycles and timing.

• Mathematical Puzzles and Games: Patterns enhance logical thinking.

IX. Student Tips & Strategies for Success:

• Time Management: Regular practice of factorization and divisibility tests.

• Exam Preparation: Memorize divisibility rules; solve PYQs for confidence.

• Stress Management: Break problems into smaller parts; stay calm during problem-solving.

X. Career Guidance & Exploration:

• For Classes 9–10:

  • Explore streams: Science, Commerce, Arts.

  • Prepare for competitive exams like NTSE, Olympiads to strengthen number sense.

• For Classes 11–12:

  • Careers in Engineering, Data Science, Computer Science rely on strong number theory.

  • Prepare for entrance exams (JEE, NEET, CUET) focusing on fundamentals.

XI. Important Notes:

• Always check the official CBSE website for syllabus updates.

• Focus on understanding the logic behind divisibility and factorization.

• Practice regularly for mastery.