Divisibility rules
Decide without dividing whether a whole number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10 by choosing the appropriate rule — the last digit (2, 5, 10), the number formed by the last two or three digits (4, 8), the sum of the digits (3, 9), or divisibility by both 2 and 3 (6) — and explain why a rule works using place value and known multiples (for example, 100 is a multiple of 4, so only the last two digits matter for 4)
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Divisibility rules means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Place-value grid (ones / tenths / hundredths); Pencil. 1. Say the goal of Divisibility rules in plain words once. 2. Adult shows 0.3 as three tenths on the grid. 3. Child builds three decimal amounts on the grid and reads them aloud. 4. Fresh check: one fresh tenths/hundredths reading. Record and stop. Done: three correct decimal readings. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Start practiceDivisibility rules practice
Practice key ideas from Divisibility rules.
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BBC Bitesize · Practice link — not the full lesson
KS3 Maths
Before you open · source notes
KS3 Maths supports Divisibility rules. An adult previews and guides; this is a learning page, not a scored quiz.
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Before you openAsk the learner one fact they learned and one question they still have.
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Public BBC Bitesize page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
BBC Bitesize. “KS3 Maths.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Use the appropriate rule to decide whether a number such as 4 536 is divisible by each of 2, 3, 4, 5, 6, 8, 9 and 10, and check one of the answers by dividing
- Explain with place value why only the last two digits decide divisibility by 4 (every hundred is a multiple of 4) and why the digit sum decides divisibility by 9 (10, 100 and 1 000 are each one more than a multiple of 9)
- Explain why a number divisible by both 2 and 3 is divisible by 6, and use a counterexample such as 12 (divisible by 2 and by 4 but not by 8) to show that combining rules only works for suitable pairs
“If your child has 1 236 stickers to share equally among 3, 4, 6 or 9 friends with none left over, can they tell which group sizes work just by looking at the digits — without doing the division?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Multiplication & Division
- Age range
- Ages 11–12
Standards