Math · Stage 5

Solve digit, last-digit and divisibility puzzles

You never divide the whole number to test it — the digits give you the clue. The last digit settles ÷2, ÷5 and ÷10, the digit-sum settles ÷3 and ÷9, and the last digit of a product comes only from the last digits you multiply.

✦ Math📘 Stage 5 · S5⏱ ~12 min🧒 Ages 9–10★ Free to start

I can solve digit, last-digit and divisibility puzzles.

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Kavi's Digit Detective 🔢

Kavi spreads out a row of big numbers 🔎. "A detective never divides the whole number to test it," hoots Kavi. "I read the clues the digits leave behind. The last digit whispers ÷2, ÷5 and ÷10. The sum of the digits whispers ÷3 and ÷9. And the last digit of a product comes only from the last digits you multiply. Crack the code and the puzzle cracks itself!"

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What your child will learn

1The last digit settles ÷2, ÷5 and ÷10You don't need the whole number — just look at the last digit. Even last digit (0,2,4,6,8) → divides by 2. Last digit 0 or 5 → divides by 5. Last digit 0 → divides by 10. Tap each clue to hear it.

2The digit-sum settles ÷3 and ÷9The last digit can't tell you about ÷3. Instead, add the digits: if the sum is a multiple of 3, the whole number is too. (And if the sum is a multiple of 9, so is the number.) Sort each number — add its digits first.

3A product's last digit comes from the last digits onlyTo find the last digit of a product, you don't need the whole answer — just multiply the last digits and keep the last digit of that. Have a go, then tap to check.

4Missing digit? Run the rule in reverseA digit puzzle hides one digit (▢) and tells you the number divides by something. Use the matching rule backwards to pin down the box. For ÷9: add the digits you can see, then top up to the next multiple of 9.

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A peek inside

Is 4,728 divisible by 3?

add the digits: 4 + 7 + 2 + 8 = 21 · 21 is a multiple of 3 (3 × 7) · so the whole number is too

Try this at home: Does 60 divide exactly by 10? (does it end in 0?) __

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Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.