Class 7 Maths Number Play Notes

Class 7 Maths Number Play Notes

1. Introduction

Chapter 6, Number Play, explores patterns in numbers, divisibility, factors, multiples, and number properties. It also introduces concepts like:

  • Odd and even numbers
  • Prime and composite numbers
  • Square and cube numbers
  • Divisibility rules
  • HCF (Highest Common Factor) and LCM (Lowest Common Multiple)
  • Patterns in numbers (arithmetic sequences, patterns in squares/cubes)

This chapter helps develop logical reasoning and number sense.

2. Key Concepts

2.1 Types of Numbers

  1. Even Numbers – divisible by 2 (e.g., 2, 4, 6)
  2. Odd Numbers – not divisible by 2 (e.g., 1, 3, 5)
  3. Prime Numbers – divisible by 1 and itself only (e.g., 2, 3, 5, 7)
  4. Composite Numbers – divisible by more than 2 numbers (e.g., 4, 6, 8, 9)
  5. Square Numbers – product of a number by itself (1²=1, 2²=4, 3²=9…)
  6. Cube Numbers – number × number × number (1³=1, 2³=8, 3³=27…)

2.2 Divisibility Rules

  • Divisible by 2: Last digit even
  • Divisible by 3: Sum of digits divisible by 3
  • Divisible by 4: Last 2 digits divisible by 4
  • Divisible by 5: Last digit 0 or 5
  • Divisible by 6: Divisible by 2 and 3
  • Divisible by 9: Sum of digits divisible by 9
  • Divisible by 10: Last digit 0

2.3 Factors and Multiples

  • Factor (Divisor): Number dividing another exactly
  • Multiple: Number obtained by multiplying by integers
  • Prime Factorization: Expressing a number as a product of prime numbers

Example:
24 = 2 × 2 × 2 × 3 = 2³ × 3¹

2.4 HCF and LCM

  • HCF (Highest Common Factor): Largest number that divides two or more numbers exactly
  • LCM (Lowest Common Multiple): Smallest number divisible by two or more numbers

Methods:

  1. Prime factorization
  2. Division method
  3. Listing multiples/factors

Example:
Find HCF & LCM of 12 and 18

  • Prime factors: 12 = 2² × 3, 18 = 2 × 3²
  • HCF = 2 × 3 = 6
  • LCM = 2² × 3² = 36

2.5 Patterns in Numbers

  • Odd/Even Patterns: Alternate odd/even numbers
  • Square/Cube Patterns:
    • Square pattern: 1, 4, 9, 16… (increase by consecutive odd numbers)
    • Cube pattern: 1, 8, 27, 64… (increase by consecutive numbers squared?)
  • Divisibility Patterns: Numbers divisible by 3 → sum of digits divisible by 3

2.6 Tricks and Tips

  • Check divisibility using last digits or sum of digits
  • Use prime factorization to find HCF & LCM quickly
  • Recognize square and cube number patterns for fast calculations
  • Observe number patterns in sequences for problem-solving

7. Real-Life Applications

  • Divisibility and factors help in splitting items evenly
  • LCM & HCF are useful in time, scheduling, and arrangements
  • Patterns in numbers help in puzzles and logical games

8. Summary Table

ConceptKey Points
Even/OddEven divisible by 2; Odd not divisible by 2
Prime/CompositePrime = only 1 & itself; Composite = more than 2 factors
Square/CubeSquare = n²; Cube = n³
DivisibilityUse rules for 2,3,4,5,6,9,10
Factors & MultiplesFactor divides; Multiple obtained by multiplication
HCF & LCMHCF = largest common factor; LCM = smallest common multiple
Number PatternsOdd/even, squares, cubes, sequences

50 Mixed-Type Questions

Section A: Multiple Choice Questions (MCQs) – 10 Questions

  1. Which of the following is a prime number?
    a) 21
    b) 17
    c) 12
    d) 15
  2. The smallest composite number is:
    a) 0
    b) 1
    c) 2
    d) 4
  3. Which of the following is a square number?
    a) 15
    b) 25
    c) 30
    d) 40
  4. The cube of 3 is:
    a) 6
    b) 9
    c) 27
    d) 18
  5. 234 is divisible by:
    a) 2 only
    b) 3 only
    c) 2 and 3
    d) 5
  6. Which number is divisible by both 2 and 5?
    a) 40
    b) 33
    c) 27
    d) 21
  7. Which of the following is an odd number?
    a) 88
    b) 97
    c) 44
    d) 120
  8. HCF of 12 and 18 is:
    a) 6
    b) 12
    c) 18
    d) 24
  9. LCM of 4 and 6 is:
    a) 12
    b) 24
    c) 18
    d) 6
  10. Which number is both a square and a cube?
    a) 16
    b) 64
    c) 125
    d) 49

Section B: Fill in the Blanks – 10 Questions

  1. The first prime number is _______.
  2. The smallest even prime number is _______.
  3. The next cube after 8 is _______.
  4. 360 is divisible by _______ (2,3,5,6)
  5. The sum of digits of 123 divisible by 3? _______
  6. HCF of 8 and 12 = _______
  7. LCM of 5 and 10 = _______
  8. The square of 15 = _______
  9. 91 is divisible by _______
  10. The factors of 20 are _______

Section C: Short Answer Questions – 10 Questions

  1. List all prime numbers between 20 and 40.
  2. Find all composite numbers between 10 and 20.
  3. Find the cube of 4.
  4. Find the square of 12.
  5. Check whether 231 is divisible by 3.
  6. Find HCF of 24 and 36 using prime factorization.
  7. Find LCM of 8 and 12 using prime factorization.
  8. Write first 5 square numbers greater than 50.
  9. Write first 5 cube numbers less than 100.
  10. Find whether 289 is a perfect square.

Section D: Long Answer / Problem-Solving – 10 Questions

  1. Find HCF and LCM of 18, 24, and 30 using prime factorization.
  2. A number is divisible by 2,3, and 5. Give an example.
  3. Find HCF of 48 and 64 using long division method.
  4. Find LCM of 15, 20 using listing multiples.
  5. A number is both a square and cube. Find the first three such numbers.
  6. Check whether 2025 is divisible by 9.
  7. Find the smallest number divisible by 2,3,5,7.
  8. A student has 24 red pencils and 36 blue pencils. She wants to make equal sets without leftover. Find number of pencils in each set using HCF.
  9. Find the sum of the first 10 square numbers.
  10. Find the sum of the first 5 cube numbers.

Section E: Application / Higher-Order Thinking – 10 Questions

  1. The sum of digits of a number = 9. Can the number be divisible by 3? Explain.
  2. A shop sells 60 chocolates and 90 candies in packets. She wants equal packets. Find maximum number of items in each packet using HCF.
  3. Find LCM of 12, 15, 20 using prime factorization.
  4. A number is divisible by 2, 3, 4, 5. Find the smallest number satisfying all conditions.
  5. Check whether 1001 is divisible by 7.
  6. Find the number of perfect cubes between 1 and 1000.
  7. A teacher divides students into groups such that each group has the same number of boys and girls without leftover. Boys = 24, Girls = 36. Find group size using HCF.
  8. Find LCM of 6, 8, 12 using listing multiples method.
  9. Identify all numbers less than 50 which are both square and cube numbers.
  10. A puzzle: The sum of two numbers = 120. HCF = 12. Find LCM.

Answers – Chapter 6: Number Play

Section A: MCQs – Answers

  1. b) 17 – 17 is divisible only by 1 and itself.
  2. d) 4 – 4 is the smallest composite number.
  3. b) 25 – 25 = 5², a perfect square.
  4. c) 27 – Cube of 3 = 3 × 3 × 3 = 27.
  5. c) 2 and 3 – 234 divisible by 2 (even) and 3 (sum of digits 2+3+4=9).
  6. a) 40 – Divisible by 2 (even) and 5 (last digit 0).
  7. b) 97 – 97 is odd.
  8. a) 6 – HCF of 12 and 18 via prime factorization: 12=2²×3, 18=2×3² → HCF=2×3=6.
  9. a) 12 – LCM of 4 and 6: 4=2², 6=2×3 → LCM=2²×3=12.
  10. b) 64 – 64 = 8² and 4³, both square and cube.

Section B: Fill in the Blanks – Answers

  1. 2 – First prime number.
  2. 2 – Only even prime number.
  3. 27 – Cube of 3.
  4. 2, 3, 5, 6 – 360 divisible by all.
  5. Yes – Sum of digits 1+2+3=6, divisible by 3.
  6. 4 – HCF of 8 and 12.
  7. 10 – LCM of 5 and 10.
  8. 225 – 15²=225.
  9. 7, 13 – 91 divisible by 7 and 13.
  10. 1, 2, 4, 5, 10, 20 – Factors of 20.

Section C: Short Answer Questions – Answers

  1. Prime numbers between 20–40: 23, 29, 31, 37
  2. Composite numbers between 10–20: 12, 14, 15, 16, 18, 20
  3. Cube of 4 = 64
  4. Square of 12 = 144
  5. 231 divisible by 3: 2+3+1=6 → divisible by 3 → Yes
  6. HCF of 24 & 36: 24=2³×3, 36=2²×3² → HCF=2²×3=12
  7. LCM of 8 & 12: 8=2³, 12=2²×3 → LCM=2³×3=24
  8. Square numbers >50: 64, 81, 100, 121, 144
  9. Cube numbers <100: 1, 8, 27, 64
  10. 289 = 17² → Perfect square

Section D: Long Answer / Problem-Solving – Answers

  1. HCF & LCM of 18, 24, 30:
  • Prime factors: 18=2×3², 24=2³×3, 30=2×3×5
  • HCF = 2×3=6
  • LCM = 2³×3²×5=360
  1. Example divisible by 2,3,5: 30
  2. HCF of 48 & 64 (division method):
  • 64 ÷ 48 = 1 remainder 16
  • 48 ÷ 16 = 3 remainder 0 → HCF = 16
  1. LCM of 15 & 20 (listing multiples):
  • Multiples of 15: 15,30,45,60,…
  • Multiples of 20: 20,40,60,… → LCM = 60
  1. Numbers both square & cube: 1 (1²=1³=1), 64 (8²=64,4³=64), 729 (27²=729,9³=729)
  2. 2025 divisible by 9: 2+0+2+5=9 → divisible by 9 → Yes
  3. Smallest number divisible by 2,3,5,7: 2×3×5×7=210
  4. Equal pencil sets:
  • HCF of 24 & 36 = 12 → 12 pencils in each set
  1. Sum of first 10 square numbers: 1²+2²+…+10²=385
  2. Sum of first 5 cube numbers: 1³+2³+3³+4³+5³=225

Section E: Application / Higher-Order Thinking – Answers

  1. Sum of digits =9 → divisible by 3: Yes, because sum divisible by 3
  2. Equal packets of chocolates & candies: HCF of 60 & 90 = 30 → 30 items per packet
  3. LCM of 12,15,20:
  • 12=2²×3, 15=3×5, 20=2²×5 → LCM=2²×3×5=60
  1. Smallest number divisible by 2,3,4,5: LCM of 2,3,4,5=60
  2. 1001 divisible by 7: 7×143=1001 → Yes
  3. Perfect cubes 1–1000: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
  4. Group size (HCF of 24 & 36) = 12 students per group
  5. LCM of 6,8,12:
  • 6=2×3, 8=2³, 12=2²×3 → LCM=2³×3=24
  1. Numbers <50 both square & cube: 1, 64 (but 64>50) → only 1
  2. Sum =120, HCF =12 → LCM = (120×HCF)/sum?
  • Let numbers = 12a, 12b → 12a + 12b = 120 → a+b=10
  • LCM = 12 × LCM(a,b) = 12 × (a×b) ???
  • If a+b=10, simplest numbers could be 4,6 → LCM(a,b)=12 → LCM numbers = 12×12=144
    ✅ So LCM = 144