Divisibility Rules

• Fast divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 — without doing long division.
• How to combine two rules (e.g. divisible by 12 = divisible by 3 AND by 4).
• Olympiad-style tricks: finding missing digits, counting how many numbers in a range satisfy a divisibility condition, and reasoning with LCM to find "smallest/largest number divisible by several numbers".

1. Divisible by 2 — last digit is even (0,2,4,6,8).
2. Divisible by 3 — sum of digits is a multiple of 3.
3. Divisible by 4 — last two digits form a multiple of 4.
4. Divisible by 5 — last digit is 0 or 5.
5. Divisible by 6 — divisible by both 2 and 3.
6. Divisible by 8 — last three digits form a multiple of 8.
7. Divisible by 9 — sum of digits is a multiple of 9.
8. Divisible by 10 — last digit is 0.
9. Divisible by 11 — (sum of digits in odd positions from the right) − (sum in even positions) is a multiple of 11 (including 0).

Is 4356 divisible by 12?

Step 1 — 12 = 3 × 4, so check divisibility by 3 AND by 4.
Step 2 — Digit sum of 4356 = 4+3+5+6 = 18, a multiple of 3. ✓
Step 3 — Last two digits are 56, and 56 ÷ 4 = 14, a whole number. ✓
Step 4 — Both conditions hold, so 4356 is divisible by 12 (4356 ÷ 12 = 363).

• Forgetting that "divisible by 12" needs BOTH the 3-rule and the 4-rule, not just one.
• Misapplying the 11-rule by not alternating signs correctly on the digits.
• Assuming divisible-by-4 also means divisible-by-8 (it doesn't — always re-check the specific rule).

• Which of 348, 522, 615 is divisible by 6?
• Find a digit to place in 7_35 so the number is divisible by 9.
• How many numbers from 1 to 100 are divisible by both 4 and 6?

Open the Practice tab for graded questions on Divisibility Rules.

• Use the platform-native live simulation (digit-rule checker / number grid highlighter) for this topic.
• Mirror / body / home activity: pick five house/shop numbers and test each against 3, 4, 6, 9, 11 rules; log results in a table.
• Voice or text reflection with AI Mentor: explain why the digit-sum trick for 3 and 9 works.

• "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.