Number Theory

Grade 6 · Mathematics

Semester 2 | Period 4 | Week 19

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Subject: Mathematics

Semester: 2

Period: 4

Week: 19

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 19
Lesson Duration: 45 minutes
Week & Period: Week 19, Period 4
Topic: Number Theory
Sub-topic: Factors, Multiples, LCM & GCF

Learning Objectives
By the end of the lesson, students should be able to:

  1. Define and identify factors and multiples of given numbers.
  2. Differentiate between prime and composite numbers.
  3. Perform prime factorization of numbers.
  4. Find the LCM (Least Common Multiple) of two or more numbers.
  5. Find the GCF (Greatest Common Factor) of two or more numbers.
  6. Solve real-life word problems involving LCM and GCF.

Previous Knowledge
Students already know multiplication tables and basic division facts.

Instructional Materials
Mathematics textbook for Grade 6, multiplication chart, factor trees, flashcards, number strips.

Lesson Development – ABC Model

A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Quick oral drill: Teacher asks students to list the first 5 multiples of 6 and 8. Discuss which multiples appear in both lists.

 

 

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definitions and Explanations

  1. Factors
  • A factor of a number is a whole number that divides it exactly without leaving a remainder.
  • Example:
    • Factors of 12 are 1, 2, 3, 4, 6, 12.
    • Factors of 20 are 1, 2, 4, 5, 10, 20.
  • Check: Multiply pairs of factors to get the original number (e.g., 2 × 6 = 12, 4 × 5 = 20).
  1. Multiples
  • A multiple of a number is obtained when the number is multiplied by whole numbers (1, 2, 3, …).
  • Example:
    • Multiples of 6 are 6, 12, 18, 24, 30, 36, ….
    • Multiples of 8 are 8, 16, 24, 32, 40, ….
  • Note: Multiples go on endlessly.
  1. Prime Numbers
  • Prime numbers are numbers with exactly two factors: 1 and itself.
  • Examples: 2, 3, 5, 7, 11, 13, 17.
  • Special Note: 2 is the only even prime number.
  1. Composite Numbers
  • Composite numbers have more than two factors.
  • Examples:
    • 4 (1, 2, 4), 6 (1, 2, 3, 6), 8 (1, 2, 4, 8).
  1. Prime Factorization
  • The process of breaking down a composite number into a product of prime numbers.
  • Factor Tree Method:
    • 36 ÷ 2 = 18 → 18 ÷ 2 = 9 → 9 ÷ 3 = 3 → 3 ÷ 3 = 1.
    • 36 = 2 × 2 × 3 × 3 = 2² × 3².
  • Another Example:
    • 60 → 2 × 30 → 2 × 3 × 10 → 2 × 3 × 2 × 5 = 2² × 3 × 5.
  1. LCM (Least Common Multiple)
  • The smallest multiple common to two or more numbers.
  • Methods:
    • Listing Multiples:
      • Multiples of 4 = 4, 8, 12, 16, 20, 24…
      • Multiples of 6 = 6, 12, 18, 24, 30…
      • Common multiples = 12, 24…
      • LCM = 12.
    • Prime Factorization:
      • Example: Find LCM of 12 and 18.
      • 12 = 2² × 3, 18 = 2 × 3².
      • Take the highest powers: 2² × 3² = 36.
  1. GCF (Greatest Common Factor)
  • The largest factor common to two or more numbers.
  • Prime Factorization Method:
    • Example: Find GCF of 12 and 18.
    • 12 = 2² × 3, 18 = 2 × 3².
    • Common factors = 2 × 3 = 6.
  • Another Example: Find GCF of 30 and 45.
    • 30 = 2 × 3 × 5.
    • 45 = 3² × 5.
    • Common = 3 × 5 = 15.

 

More Word Problems

  1. Two bells ring at intervals of 12 minutes and 18 minutes. After how many minutes will they ring together again?
    • Solution: LCM of 12 and 18 = 36 minutes.
  2. A farmer has 24 oranges and 36 mangoes. He wants to pack them in baskets with equal number of fruits and no leftovers. What is the greatest number of fruits per basket?
    • Solution: GCF of 24 and 36 = 12 fruits per basket.
  3. A school has two buses: one comes every 20 minutes, the other every 30 minutes. If they both arrive at 8:00 am, when will they meet again?
    • Solution: LCM of 20 and 30 = 60 minutes → 9:00 am.
  4. Three children are skipping in turns. The first skips every 4 jumps, the second every 6 jumps, and the third every 8 jumps. After how many jumps will they all skip together?
    • Solution: LCM of 4, 6, 8 = 24 jumps.

 

Learners’ Activities (Expanded)

  • In groups, learners will:
  1. Draw factor trees for numbers 24, 36, 48, and 60.
  2. List first 10 multiples of 3, 5, and 7.
  3. Use prime factorization to find LCM and GCF of:
    • (a) 12 and 20
    • (b) 15 and 25
    • (c) 18 and 24
  4. Solve at least 3 real-life word problems on LCM and GCF.

 

Assessment Checks

  1. Teacher asks:
    • What is the difference between a factor and a multiple?
    • Why is 7 a prime number but 9 is not?
    • Find the GCF of 16 and 20.
    • Find the LCM of 8 and 10.
  2. Quick quiz problems:
    • (i) Write the first 5 multiples of 9.
    • (ii) List all factors of 28.
    • (iii) Find prime factorization of 72.
    • (iv) A farmer plants maize every 15 days and cassava every 20 days. After how many days will he plant both crops on the same day?

 

Notes (Expanded & Detailed)

  • Factors are useful for dividing items into equal groups.
  • Multiples help us understand repeated addition and cycles.
  • Prime factorization breaks a number into its building blocks.
  • LCM is used when events repeat and we want to know when they will happen together (bells, buses, schedules).
  • GCF is used when dividing items into equal groups without leftovers (sharing fruits, arranging items).

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher revises definitions of factors, multiples, LCM, and GCF.

Evaluation Method (Expanded):
Exit slip/quiz:

  1. List factors of 20.
  2. Write first 5 multiples of 9.
  3. Find LCM of 8 and 12.
  4. Find GCF of 24 and 36.

Teacher will collect slips and provide oral feedback.

Assignment (Expanded):
Solve:

  1. Find LCM of 15 and 20.
  2. Find GCF of 42 and 56.
  3. Two traffic lights blink every 30 seconds and 45 seconds. After how many seconds will they blink together again?

Follow-up Activity:
Students practice with classmates’ birthdays to find LCM and GCF of dates.

Differentiation / Inclusive Strategies
Use multiplication tables and visual factor trees for learners who need support. Challenge advanced learners with larger numbers.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low