Factors of a Number

• A factor divides a number exactly (remainder 0).
• Find all factors by multiplication pairs.
• Find common factors of two numbers for sharing problems.

Level 1 — Definition

If 12 ÷ 3 = 4 with no remainder, then 3 and 4 are factors of 12.

Verbal: Factors are exact divisors — they split a number into equal whole parts.

Level 2 — Pair method for 24

All factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Level 3 — Common factors

Common factors of 12 and 18: 1, 2, 3, 6. HCF = 6.

Level 4 — Indian context

48 Diwali diyas arranged in equal rows on a rangoli — possible rows: 2, 3, 4, 6, 8, 12, 16, 24 (all factors of 48).

NCERT anchor: Math-Magic 4, Ch 11 — Tables and Shares; Ch 14 — Play with Patterns (equal groups and arrays)

Find all factors of 36

Step 1 — Pairs: 1×36, 2×18, 3×12, 4×9, 6×6.
Step 2 — List: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 3 — Verify: 36 ÷ 9 = 4 ✓
Answer: 9 factors

Common factors of 20 and 30

Step 1 — Factors of 20: 1, 2, 4, 5, 10, 20.
Step 2 — Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Step 3 — Common: 1, 2, 5, 10.
Answer: HCF = 10

• List all factors of 20.
• Is 7 a factor of 42? (yes — 42 ÷ 7 = 6)
• Common factor of 15 and 25? (5)
• Stretch: A farmer has 60 mango saplings. He wants equal rows with more than 1 row and fewer than 60 rows. How many different row counts are possible? (8: 2,3,4,5,6,10,12,15,20,30 — actually count factors excluding 1 and 60 = 8 ways)

Revision tip: Write multiplication pairs in two columns that meet in the middle — nothing gets missed.

Open the Practice tab for graded questions on Factors of a Number.

• Use the platform-native live simulation or PhET-style tool for this topic (number line, Venn, physics playground, molecule builder, sensor dashboard, etc.).
• Mirror / body / home activity: physically do the concept (count objects, measure, role-play) and photograph or describe for portfolio.
• Voice or text reflection with AI Mentor: explain the concept to a younger student or family member.

• "Explain this concept to a Class 6 student using one real example from an Indian home, school, market, or festival."
• "What is one common mistake students make here, and how would you catch yourself making it?"
• Stretch: "How does this connect to coding, robotics, money, health, environment, or a future career?"

• Complete the core practice + one extension activity (photo, table, short reflection, or mini-project) for base XP + topic badge.
• 5-7 day streak or family discussion note = multiplier + visible artifact in parent/principal dashboard.
• Best real-world application stories (anonymised) featured on class or national leaderboard.

• One hands-on project or measurement using the Drishti kit or household items that makes the concept physical.
• Direct link to at least one Future Skill track (Money Management, Green Tech, Cyber Defenders, Micro-Entrepreneurship, AI Mastery, Sustainable Living, Personality Development).
• Coding extension where relevant (simple script, simulation, or data logging).

This material emphasises experiential "learning by doing", competency (apply/create/analyse), vocational exposure, critical thinking, and multidisciplinary connections. Designed to feed live worlds, AI Mentor (with memory), gamification, robotics, parent analytics, and future skills — not just exam prep.

Portfolio Evidence Idea: Your photo/table/reflection/project + one sentence on "How this helps me in real life or a possible future path."

Open the Practice tab for aligned questions (easy/medium/hard + case-based) with full AI scaffolding.

See curriculum for cross-links and the full future-skills/robotics chapters.