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Class 7 → Mathematics → Chapter 6: Number Play
I. Chapter Summary:
The chapter Number Play explores interesting properties and patterns of numbers. It introduces students to concepts such as factors, multiples, divisibility rules, prime and composite numbers, and common factors like HCF (Highest Common Factor) and LCM (Least Common Multiple). Students also learn how to apply these concepts in solving real-life problems. This chapter builds strong number sense and logical reasoning skills.
II. Key Concepts Covered:
1. Factors and Multiples
- Factors: Numbers that divide a number exactly
- Multiples: Result of multiplying a number
2. Prime and Composite Numbers
- Prime Numbers: Only two factors (1 and itself)
- Composite Numbers: More than two factors
3. Even and Odd Numbers
- Even numbers divisible by 2
- Odd numbers not divisible by 2
4. Divisibility Rules
- By 2 → Last digit even
- By 3 → Sum of digits divisible by 3
- By 5 → Ends in 0 or 5
5. HCF (Highest Common Factor)
Greatest number that divides two or more numbers.
6. LCM (Least Common Multiple)
Smallest number divisible by given numbers.
7. Number Patterns
Recognizing patterns in numbers and sequences.
III. Important Questions:
(A) MCQs (1 Mark):
- Which is a prime number?
(a) 4
(b) 6
(c) 7 ✅
(d) 9 - The HCF of 12 and 18 is:
(a) 2
(b) 3
(c) 6 ✅
(d) 9 - The LCM of 4 and 5 is:
(a) 10
(b) 20 ✅
(c) 15
(d) 25 - Which number is divisible by 5?
(a) 23
(b) 45 ✅
(c) 37
(d) 41
(B) Short Answer Questions (2/3 Marks):
- Define factors and multiples with examples.
- What are prime numbers? Give examples.
- Find HCF of 8 and 12.
- Write the divisibility rule of 3.
(C) Long Answer Questions (5 Marks):
- Explain prime and composite numbers with examples.
- Find HCF and LCM of given numbers using suitable methods.
- Explain divisibility rules with examples.
- Solve problems based on number patterns.
(D) HOTS Questions:
- Can a number be both prime and even? Explain.
- Why is LCM useful in solving real-life problems like scheduling events?
IV. Key Formulas/Concepts:
HCF and LCM Relationship
$text{HCF} times text{LCM} = text{Product of the numbers}$
Example 1: HCF
$text{HCF of 12 and 18} = 6$
Example 2: LCM
$text{LCM of 4 and 5} = 20$
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):
| Unit/Chapter | Estimated Marks | Type of Questions Typically Asked |
|---|---|---|
| Number Play | 6–8 Marks | MCQs, Short Answer, Numerical-based |
Note: This is an estimate. Actual marks distribution may vary.
VII. Previous Year Questions (PYQs):
1 Mark:
- Identify a prime number from given options. (2019)
2/3 Marks:
- Find HCF of two numbers. (2020)
- State divisibility rule of 5. (2021)
5 Marks:
- Find HCF and LCM of given numbers. (2022)
VIII. Real-World Application Examples:
- Finding common time for events using LCM
- Dividing items equally using HCF
- Identifying patterns in data
- Scheduling and planning tasks
IX. Student Tips & Strategies for Success:
Time Management:
- Practice factorization daily.
Exam Preparation:
- Learn divisibility rules thoroughly.
- Practice HCF and LCM problems.
Stress Management:
- Solve problems step-by-step.
- Avoid calculation mistakes.
X. Career Guidance & Exploration:
- Science Stream: Mathematics, Engineering
- Commerce Stream: Accounting, Finance
- Arts Stream: Statistics, Data Analysis
Entrance Exams (Basic Awareness):
- JEE (Engineering)
- CA Foundation
XI. Important Notes:
- Understand concepts of factors and multiples clearly.
- Practice regularly for accuracy.
- Learn divisibility rules.
- Refer to NCERT textbook.
- Revise frequently.