Mathematics · Class 6

Active learning ideas

Highest Common Factor (HCF)

Active learning works well for HCF because students often struggle with abstract number concepts when taught only through rules. When children physically group tiles or race through division steps, they see why the largest common factor matters in sharing. Concrete and kinaesthetic activities turn a dry procedure into a meaningful problem-solving experience.

• CBSE Learning Outcomes
• NCERT: Playing with Numbers - HCF and LCM - Class 6

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Tile Grouping: Finding HCF Visually

Provide pairs with tiles or blocks representing two numbers, like 12 and 18 tiles. Students arrange into largest equal groups for both sets simultaneously, noting group size as HCF. They verify by division and record observations.

How can we use factors to find the largest possible shared unit between two quantities?

Facilitation Tip

During Tile Grouping, ask each pair to record the largest tile bundle size they can form before moving to the next number pair.

What to look for

Present students with three numbers, e.g., 24, 36, and 48. Ask them to find the HCF using prime factorization and then verify their answer using the division method. Observe their process and check for correct application of both methods.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 25 min · Small Groups

Prime Factorisation Relay: Team Challenge

In small groups, students line up. First member factorises one number on chart paper, passes to next for second number, then group identifies common primes for HCF. Discuss and repeat with new numbers.

Differentiate between common factors and the highest common factor.

Facilitation Tip

For Prime Factorisation Relay, provide coloured pencils so teams can circle common primes and cross out unused powers clearly.

What to look for

On a small slip of paper, ask students to write down one real-world scenario where finding the HCF would be useful, and briefly explain why. For example, 'Dividing 10 apples and 15 oranges into the largest possible equal fruit baskets.'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 35 min · Pairs

Division Ladder Race: Pairs Competition

Pairs race to complete division ladders for given numbers, like 36 and 48. One divides while partner checks remainders. First correct pair shares steps with class.

Design a real-world problem that requires finding the HCF for its solution.

Facilitation Tip

In Division Ladder Race, insist students write each division step fully before passing the sheet to their partner.

What to look for

Pose the question: 'How is finding the HCF similar to finding the largest common unit when sharing items?' Facilitate a class discussion, encouraging students to use examples like sharing sweets or dividing a rope into equal lengths.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 40 min · Whole Class

Real-Life Problem Design: Whole Class

Pose scenario like dividing 60 kg rice into bags for two shops. Class brainstorms HCF uses, solves collectively, then designs own problems for gallery walk.

How can we use factors to find the largest possible shared unit between two quantities?

Facilitation Tip

When designing Real-Life Problems, remind students to include both numbers and the exact HCF they calculated.

What to look for

Present students with three numbers, e.g., 24, 36, and 48. Ask them to find the HCF using prime factorization and then verify their answer using the division method. Observe their process and check for correct application of both methods.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with visual grouping before symbols so students understand the meaning of 'common' and 'largest'. Alternate between prime factorisation and division methods so learners see how different tools solve the same problem. Avoid rushing to algorithms; let students discover patterns through guided discovery rather than rote memorisation. Research shows that when students explain their steps aloud, misconceptions surface early and can be corrected through peer discussion.

Successful learning looks like students confidently explaining why the HCF of 12 and 18 is 6, not 1, and choosing the most efficient method for different problems. You will notice students using correct terminology like 'common prime factors' and 'lowest power' while working in teams. By the end, every learner should connect the concept to real-life situations such as equal distribution of resources.

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Watch Out for These Misconceptions

• During Tile Grouping, watch for students who assume the HCF is always 1 because they stop at the smallest bundle size rather than the largest shared bundle.

  Ask students to compare their largest bundle across both number sets and explain why a bigger shared bundle is possible; use questions like 'Can you make bundles of 6 tiles from both 12 and 18?'

• During Prime Factorisation Relay, watch for students who copy all common primes without comparing powers, writing HCF(12,18) as 2×3×3=18 instead of 2×3=6.

  Have teams use different coloured markers for each prime and physically circle the term with the lower exponent; ask them to read their answer aloud while pointing to the circled terms.

• During Division Ladder Race, watch for students who switch to repeated subtraction instead of division, writing 18-12=6, then 12-6=6, and calling 6 the HCF.

  Stop the race immediately and ask partners to check their division steps; display a correct division ladder on the board and ask students to explain why 12÷6=2 and not 12-6=6.

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Methods used in this brief

• Problem-Based Learning