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Session 32: Highest Common Factor (HCF)

Session Title

The  Greatest Common

Objective

By the end of this session, students will be able to:


1. Understand the concept of HCF and its applications.


2. Develop logical reasoning and problem-solving skills.


3. Enhance collaboration and communication through activities.


4. Foster patience and perseverance in problem-solving.

Topics/Concept

Highest Common Factor (HCF) – Finding HCF using prime factorization and division method.

Material Required

Board,

Chalk,Board Chart, Marker,Chalk  Chart  Marker  pebbles/ beads,beads  paper glass(50)

Box 

Methodology

Activity-based and experiential learning


SEL elements like teamwork, patience, and self-confidence


Real-life applications to make the concept meaningful

Session Plan (120 MIn)

 90

minutes

Intro  ActivityActivity(45 minutes) 

WORKINGWorking MODEL:Model  ( 3025 minutes )


1.

A table with numbers 1 to 50 written on it

2.

 Paper cups or glasses placed in front of each number

3.

A box of beads (or small objects like pebbles)

4.

Invite a student and give them the box of beads.

5.

Ask them to place one bead in every glass where the number is divisible by 5.

(The glasses at 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 will get a bead.

)

6.

 Next, ask the student to place a bead in every glass where the number is divisible by 10.

(The glasses at 10, 20, 30, 40, 50 will now have two beads (one from 5’s and one from 10’s).


The HCF is the highest number that has multiples of beads.


Here, HCF of 5 and 10 = 10.



Group

GROUP WORK:Work (20 Minutes)


1.

Divide students into small groups. Give each group 4 number cards. Example: 12, 18, 24, 30.

2.

Ask them to find all factors of their numbers and write them down.

Answer:-

    Factors of 12: 1, 2, 3, 4, 6, 12

    Factors of 18: 1, 2, 3, 6, 9, 18

    Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

    Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

    3.

       Now, ask them to circle the common factors. Common factors: 1, 2, 3, 6

      4.

       Guide them to find the highest common factor. HCF = 6

      Discussion: What do you notice? Why is this factor important?


      Answer: The HCF is the largest number that divides all given numbers without a remainder.



      Main Activity.(35 minutes)

      Main Topic/ Activity.


      Story: "The Royal Feast Challenge" ( 30 minutes)



      King Aryan was preparing a grand feast for his kingdom. He wanted to serve food equally among the guests without anything left over.


      The royal chef, Ravi, had collected:


      48 loaves of bread


      72 bowls of soup



      The king asked, "How can we arrange these in equal groups so that each group gets the same amount of bread and soup?"


      The villagers were excited to solve this puzzle. Can you help them?


      Your Challenge:


      1.

      Find the Highest Common Factor (HCF) of 48 and 72 to determine the number of groups.

      2.

      Once you find the HCF, divide the food equally into that many groups.

      3.

       How many loaves of bread and bowls of soup will each group get?

      Think & Solve:


      Step 1: Find the factors of 48 and 72.

      Step 2: Identify the common factors.

      Step 3: Find the highest common factor (HCF).

      Step 4: Divide the food accordingly.

      Review Questions(5

      Expected Learning  Outcome:

      Knowledge building-

      minutes)
      • What

        Definition ofdoes HCF

        stand for?
      • How

        Whyis HCF isdifferent important

        from

      Different methods to find HCF

      LCM?

      Skill Building-

        Logical thinking

        Problem solving skill

        Review Questions/Assessment/Tasks 


        Follow up TasksTask(10
        minutes)

        Home work   (10 minutes)


        1. A school is making groups of students for a competition. There are 32 boys and 48 girls. Each group must have the same number of boys and girls.

          • What is the maximum number of groups that can be formed?

          • How many boys and girls will be in each group?



        1. A fruit seller has 40 apples and 64 oranges. He wants to pack them into baskets, keeping the same number of apples and oranges in each basket.


          • How

            many apples and oranges will be in each basket?

        What is the maximum number of baskets he can make?

        Expected Learning  Outcome:

        Knowledge building-

          Definition of HCF


          Why

            HCF is important

            HowDifferent manymethods applesto andfind oranges will be in each basket?HCF

            Skill Building-

            • Logical thinking

            Problem solving skill





             

             

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