Identifying Factors and Multiples

Active learning works for identifying factors and multiples because students need to physically manipulate numbers to see the relationships between them, not just memorise rules. Concrete materials like tiles or counters help them visualise division and multiplication in ways that abstract explanations cannot. These activities build confidence as students discover patterns themselves rather than having them told.

• Class 5
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Compare the properties of factors and multiples for a given number, identifying similarities and differences.
2. Explain the relationship between a number, its factors, and its multiples, using examples.
3. Calculate all factors of a given number up to 100.
4. Generate the first ten multiples of a given number up to 100.
5. Classify numbers as prime or composite based on their number of factors.

Think-Pair-Share

⏱ 35 min·Small Groups

Hands-On: Tile Grouping

Give each small group 24-48 counters or tiles. Ask them to group in different ways to find factor pairs, like 3x8 or 4x6 for 24. Record pairs on chart paper and discuss why 1x24 works. Extend to predict factors for larger sets.

Prepare & details

Compare the characteristics of factors and multiples of a given number.

Facilitation Tip: During Tile Grouping, observe how students arrange tiles to form rectangles, noting if they consider both 1xN and Nx1 as valid groupings to address the misconception that factors must be smaller.

Setup: Works in standard Indian classroom seating without moving furniture — students turn to the person beside or behind them for the pair phase. No rearrangement required. Suitable for fixed-bench government school classrooms and standard desk-and-chair CBSE and ICSE classrooms alike.

Materials: Printed or written TPS prompt card (one open-ended question per activity), Individual notebook or response slip for the think phase, Optional pair recording slip with 'We agree that...' and 'We disagree about...' boxes, Timer (mobile phone or board timer), Chalk or whiteboard space for capturing shared responses during the class share phase

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Simulation Game

⏱ 30 min·Whole Class

Simulation Game: Factor Bingo

Prepare bingo cards with numbers 1-50. Call out a number, students mark its factors on their card. First to complete a line shouts 'Factors!'. Review marked factors as a class to reinforce lists.

Prepare & details

Explain why every number is both a factor and a multiple of itself.

Facilitation Tip: For Factor Bingo, circulate to listen for students justifying why a number is or isn’t a factor, reinforcing precise mathematical language.

Setup: Standard classroom — rearrange desks into clusters of 6–8; adaptable to rooms with fixed benches using in-seat group structures

Materials: Printed A4 role cards (one per student), Scenario brief sheet for each group, Decision tracking or event log worksheet, Visible countdown timer, Blackboard or chart paper for recording simulation events

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Think-Pair-Share

⏱ 25 min·Pairs

Pairs: Multiples Chain

In pairs, start with a number like 7. One student says next multiple, partner continues up to 100. Switch roles after 10 multiples. Pairs then compare chains and spot patterns with neighbours.

Prepare & details

Predict how the number of factors changes as a number increases in value.

Facilitation Tip: In the Multiples Chain activity, step in when pairs struggle to generate multiples beyond 100 to ensure they connect the concept to real-world contexts like counting money or measuring.

Setup: Works in standard Indian classroom seating without moving furniture — students turn to the person beside or behind them for the pair phase. No rearrangement required. Suitable for fixed-bench government school classrooms and standard desk-and-chair CBSE and ICSE classrooms alike.

Materials: Printed or written TPS prompt card (one open-ended question per activity), Individual notebook or response slip for the think phase, Optional pair recording slip with 'We agree that...' and 'We disagree about...' boxes, Timer (mobile phone or board timer), Chalk or whiteboard space for capturing shared responses during the class share phase

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Factor Challenges

Set up stations: 1) list factors with divisibility checks, 2) model with drawings, 3) match numbers to factor counts, 4) generate multiples sequences. Groups rotate, recording one insight per station.

Prepare & details

Compare the characteristics of factors and multiples of a given number.

Facilitation Tip: During Factor Challenges, provide scaffolding for students who list factors randomly by guiding them to use the smallest factor first to build systematic thinking.

Setup: Designate four to six fixed zones within the existing classroom layout — no furniture rearrangement required. Assign groups to zones using a rotation chart displayed on the blackboard. Each zone should have a laminated instruction card and all required materials pre-positioned before the period begins.

Materials: Laminated station instruction cards with must-do task and extension activity, NCERT-aligned task sheets or printed board-format practice questions, Visual rotation chart for the blackboard showing group assignments and timing, Individual exit ticket slips linked to the chapter objective

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Teaching This Topic

Teachers should approach this topic by first letting students explore without formal definitions, allowing them to discover relationships through hands-on work. Avoid rushing to formalise the concept of factors and multiples before students have a strong intuitive grasp. Research shows that students who struggle often benefit from visual and kinaesthetic methods like arrays and counters, which help bridge the gap between concrete and abstract thinking.

What to Expect

Successful learning looks like students confidently listing factors and multiples for any given number, explaining why 1 and the number itself are always included, and distinguishing between prime and composite numbers without hesitation. They should also articulate the difference between factors of a number and factors of its multiples, showing clear number sense.

Watch Out for These Misconceptions

Common Misconception

During Tile Grouping, watch for students who exclude a 1xN arrangement when forming rectangles, as this reveals the misconception that factors must always be smaller than the number.

What to Teach Instead

Use the tile arrays to explicitly show that a single row of N tiles still represents a factor pair (1 and N), reinforcing that every number is a factor of itself by creating a square array when appropriate.

Common Misconception

During Factor Bingo, watch for students who incorrectly mark a number as a factor of its multiple because it appears in the multiple's factor list.

What to Teach Instead

Have students compare the factor lists of a number and its multiple side-by-side during the game, prompting them to notice that the multiple's factors include additional numbers beyond the original number's factors.

Common Misconception

During the Multiples Chain activity, watch for students who claim prime numbers have no factors after seeing them generate only 1 and themselves.

What to Teach Instead

Ask students to use counters to form arrays for prime numbers, guiding them to see that the only possible rectangles are 1xN, confirming that primes have exactly two factors: 1 and themselves.

Assessment Ideas

Quick Check

After Tile Grouping, write the number 18 on the board and ask students to write down three factors and three multiples of 18, then review answers collectively to check their understanding of both concepts.

Exit Ticket

During Factor Bingo, give each student a card with a number (e.g., 15, 24, 7) and ask them to list all factors and state whether it is prime or composite, explaining their reasoning in one sentence before leaving.

Discussion Prompt

After the Multiples Chain activity, pose the question: 'Why is every number a factor and a multiple of itself?' Allow students to discuss in pairs, then call on a few pairs to share explanations, guiding them toward the definitions of factor and multiple as they reflect on their chain work.

Extensions & Scaffolding

• Challenge students to find a number with exactly 8 factors and explain how they know their list is complete.
• For students who struggle, provide partially completed factor lists to help them see the pattern of increasing factors.
• Deeper exploration: Ask students to explore numbers that have the same number of factors as their age, creating a personal connection to the concept.

Key Vocabulary

Factor	A factor is a whole number that divides another whole number exactly, with no remainder. For example, 1, 2, 5, and 10 are factors of 10.
Multiple	A multiple is the result of multiplying a whole number by another whole number. For example, 10, 20, and 30 are multiples of 10.
Prime Number	A prime number is a whole number greater than 1 that has only two factors: 1 and itself. Examples include 2, 3, 5, and 7.
Composite Number	A composite number is a whole number greater than 1 that has more than two factors. Examples include 4, 6, 8, 9, and 10.