Primes and Divisibility

• the core idea behind Primes and Divisibility and how it fits inside Number Theory Basics.
• Mastering Primes and Divisibility sharpens your problem-solving toolkit for olympiad-style questions beyond routine NCERT problems.
• A clear worked example you can copy into your notebook.

1. Prime numbers have exactly two divisors (1 and itself); every other number >1 is composite.
2. Divisibility rules (by 2,3,4,5,9,11) let you test large numbers without long division.
3. Prime factorization: every integer >1 is a unique product of primes (Fundamental Theorem of Arithmetic).
4. Number of divisors: if n = p1^a1 · p2^a2 · ... then divisor count = (a1+1)(a2+1)....

Find the number of divisors of 360.

Step 1 — factorize: 360 = 2^3 x 3^2 x 5^1
Step 2 — apply formula: (3+1)(2+1)(1+1) = 4 x 3 x 2
Step 3 — multiply: 24
Step 4 — answer: 360 has 24 divisors

• Forgetting to add 1 to each exponent in the divisor-count formula.
• Treating 1 as a prime number (it is neither prime nor composite).
• Missing a prime factor when factorizing large numbers.

• List all primes between 1 and 20.
• Find the prime factorization of 240.
• How many divisors does 196 have?

Open the Practice tab for graded questions on Primes and Divisibility.

• 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.