Mathematics · Class 6
Playing with Numbers
Factors, multiples, HCF, LCM, prime factorisation, and divisibility tests.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
A prime number has exactly two factors: 1 and itself. 1 is neither prime nor composite.
This chapter explores factors, multiples, prime and composite numbers, divisibility tests, HCF, LCM, and prime factorisation — tools used throughout school mathematics.
Factors and Multiples
- Factor divides the number exactly (remainder 0)
- Multiple = number × any whole number
- Every number is a multiple of itself and 1
Divisibility Tests
- By 2: last digit even
- By 3: sum of digits divisible by 3
- By 5: last digit 0 or 5
- By 9: sum of digits divisible by 9
- By 10: last digit 0
HCF and LCM
HCF
Highest Common Factor — largest common factor
LCM
Lowest Common Multiple — smallest common multiple
Relationship
HCF × LCM = product of two numbers (for two numbers)
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Prime Factorisation
Find prime factorisation of 84.
- 184 = 2 × 42
- 242 = 2 × 21
- 321 = 3 × 7
Answer
84 = 2² × 3 × 7
Example 2: HCF and LCM
Find HCF and LCM of 12 and 18.
- 112 = 2²×3
- 218 = 2×3²
- 3HCF = 2×3 = 6
- 4LCM = 2²×3² = 36
Answer
HCF = 6, LCM = 36
Key Points to Remember
- ✓ Use factor tree for prime factorisation
- ✓ HCF for grouping/dividing; LCM for simultaneous events
- ✓ Co-prime numbers have HCF = 1
Exam Tips
- • Show prime factorisation steps for full marks
- • Verify: HCF × LCM = a × b
Practice MCQs — Playing with Numbers
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Smallest prime number is: