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Class 6 → Mathematics → Chapter 5: Prime Time
I. Chapter Summary:
The chapter Prime Time focuses on understanding prime numbers and their importance in mathematics. It introduces concepts such as prime and composite numbers, factorization, and the use of prime factorization to find HCF (Highest Common Factor) and LCM (Least Common Multiple). Students learn how numbers can be broken into their prime factors and how these concepts are applied in solving problems efficiently.
II. Key Concepts Covered:
1. Prime Numbers
Numbers that have exactly two factors: 1 and itself.
Example: 2, 3, 5, 7
2. Composite Numbers
Numbers that have more than two factors.
Example: 4, 6, 8, 9
3. Prime Factorization
Expressing a number as a product of its prime factors.
4. Factor Tree Method
A method to find prime factors using a tree diagram.
5. HCF (Highest Common Factor)
Largest number that divides two or more numbers.
6. LCM (Least Common Multiple)
Smallest number divisible by given numbers.
7. Co-prime Numbers
Numbers having only one common factor (1).
III. Important Questions:
(A) MCQs (1 Mark):
- Which is a prime number?
(a) 4
(b) 6
(c) 11 ✅
(d) 12 - The smallest prime number is:
(a) 0
(b) 1
(c) 2 ✅
(d) 3 - Which is a composite number?
(a) 3
(b) 5
(c) 9 ✅
(d) 7 - Co-prime numbers have:
(a) Many factors
(b) One common factor (1) ✅
(c) Same factors
(d) No factors
IV. Short Answer Questions (2/3 Marks):
- Define prime numbers with examples.
- What is prime factorization?
- Find prime factors of 12.
- What are co-prime numbers?
V. Long Answer Questions (5 Marks):
- Explain prime and composite numbers with examples.
- Find HCF and LCM using prime factorization.
- Explain factor tree method with example.
- Solve problems based on co-prime numbers.
VI. HOTS Questions:
- Why is 1 not considered a prime number?
- How does prime factorization help in simplifying calculations?
VII. Key Formulas/Concepts:
Prime Factorization Concept
Number=Product of prime factors
HCF and LCM Relationship
HCF × LCM = Product of the numbers
Example:
- Prime factors of 12 = 2 × 2 × 3
- HCF of 12 and 18 = 6
- LCM of 4 and 5 = 20
VIII. Deleted Portions (CBSE 2025–2026):
No portions have been deleted from this chapter as per the rationalized NCERT textbooks.
IX. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):
| Unit/Chapter | Estimated Marks | Type of Questions Typically Asked |
|---|---|---|
| Prime Time | 5–7 Marks | MCQs, Short Answer, Numerical-based |
Note: This is an estimate. Actual marks distribution may vary.
X. Previous Year Questions (PYQs):
1 Mark:
- What is a prime number? (2019)
2/3 Marks:
- Find prime factors of a number. (2020)
- Define co-prime numbers. (2021)
5 Marks:
- Find HCF and LCM using prime factorization. (2022)
XI. Real-World Application Examples:
- Dividing objects into equal groups
- Cryptography (advanced use of prime numbers)
- Simplifying calculations
- Scheduling events
XII. Student Tips & Strategies for Success:
Time Management:
- Practice factorization daily.
Exam Preparation:
- Learn prime numbers up to 50.
- Practice HCF and LCM problems.
Stress Management:
- Solve step-by-step.
- Avoid calculation mistakes.
XIII. Career Guidance & Exploration:
- Science Stream: Mathematics, Computer Science
- Commerce Stream: Accounting
- Arts Stream: Statistics
Entrance Exams (Basic Awareness):
- Olympiads
- NTSE
XIV. Important Notes:
- Remember prime numbers carefully.
- Practice factor trees regularly.
- Understand concepts clearly.
- Refer to NCERT textbook.
- Revise frequently.