Session 32: Highest Common Factor (HCF)

Introduction Activity (10

Minutes)

GameWORKING Time : Pass pass 

In "Pass Pass," children form a circle. A target number( Eg: multiple of 2 or 3) is chosen. Starting with the first child, they count aloud in sequence. When a child's count reaches a multiple of the target number, they say "Pass" instead of the number(Eg : target number is 5. 1,2,3,4,pass,6,7.....) The next child continues the count. The game continues until only one child remains.(NB: Change the number after each round)

Main Activity

Tell a short story:- ( 20 minutes )

Two friends, Arya and Rahul, love visiting a park. Arya visits every 3 days, and Rahul visits every 4 days. If both visit the park today, when will they meet again?

Ask students to think and predict: “Will they meet again in a week? In 10 days?”

Guide them to count the days until both are at the park together (on the 12th day).

Explain numbers at the Least Common Multiple (LCM) of 3 and 4 is 12—the smallest number that both 3 and 4 can divide into evenly.

DEMO TIME MODEL: ( 30 minutes )

1. DrawA atable numberwith gridnumbers 1 to 50 written on the floor (1–50)it

2. CallPaper outcups twoor numbersglasses (e.g.,placed 4in andfront 6)of each number

3. StudentsA takebox turnsof hopping on the multiplesbeads (4,or 8,small 12…objects andlike 6, 12, 18…)pebbles)

4. TheInvite firsta commonstudent and give them the box of beads.

5. Ask them to place one bead in every glass where the number theyis stepdivisible onby 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 LCM 

 ( NB: Repeat the activity with differenthighest number )that has multiples of beads.

Here, HCF of 5 and 10 = 10.

TIMEGROUP TO SOLVE:WORK: ( 20 Minutes)

Give1. simple examples: ( DevideDivide students into small groups)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:-

• LCMFactors of 212: and1, 52, 3, 4, 6, 12

→Factors Multiples: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, 12…)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 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 (5, 10, 15…) → LCM is 10.soup?"

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

• 
  

  LCMYour Challenge:

  
  

  1. Find the Highest Common Factor (HCF) of 648 and 872 to determine the number of groups.

→2. Multiples:Once (6,you 12,find 18,the 24…)HCF, anddivide (8,the 16,food 24…)equally →into LCM is 24.

• A bell rings every 6 minutes, and another bell rings every 8 minutes. After howthat many minutes will both bells ring together?groups.

• A school organizes a sports day every 5 years, and a cultural fest every 7 years.3. How many yearsloaves laterof bread and bowls of soup will botheach eventsgroup happen together again?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.

 

Expected Learning  Outcome:

Knowledge building-

• ConceptDefinition of LCMHCF

• MethodWhy HCF is important

• Different methods to find LCMHCF

Skill Building-

• Logical thinking

• StrengthensProblem speedsolving and accuracy

• Team work skill

Review Questions/Assessment/Tasks 

Ask: What strategies helped you solve the problems quickly?

Encourage peer teaching—students explain their solutions to classmates.

Follow up TaskTasks 

Home work:work  ( 10 minutes)

1. 1.TwoA farmersschool plantis crops—onemaking plantsgroups everyof 9students days,for a competition. There are 32 boys and the48 othergirls. everyEach 12group days.must In how many days will they plant onhave the same daynumber again?of boys and girls.

1. 
   What is the maximum number of groups that can be formed?

2. 2.TwoHow busesmany leaveboys aand stationgirls atwill be in each group?

2. A fruit seller has 40 apples and 64 oranges. He wants to pack them into baskets, keeping the same time—onenumber afterof 12apples minutes,and oranges in each basket.

1. What is the othermaximum afternumber 15of minutes.baskets Whenhe can make?

2. How many apples and oranges will theybe leavein togethereach again?basket?